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ndwareinitializedas0.If,thecorrespondingiscalculated,andtheballcross-sectionwithangleisdeterminatewhetheritintersectstriangularfacets.Theintersectedtrianglesfacetsareputintothecollections..if,thealgorithmisend.
If,thecorrespondingiscalculated..if,itgoestostep2,
Iftheindexnumber(isthemaximumnumberoftriangularfacets),thecorrespondingvariablesu,vandtarecalculatedbyusingthemethodproposedinSection2..if,andthealgorithmreturnstostep3.
Ifthevariablesu,vandtdonotmeettheintersectionconditions,.Thenisafeaturevectorof3Dmodel.
ThealgorithmflowisshowninFig.7.Thevariablesl,wandkrepresenttheindexnumbersofgraticuleandtriangularfacetswhileandrepresentthemaximumnumbersofgraticuleandtriangularfacets.Thevariabletisthedistancefromtheintersectiontooriginwhileisthemaximumdistance.
Fig.7Flowofprojectionray-basedalgorithm
本篇论文出处 http://www.sxsky.net/xie/070112780.html
Supposingthenumberofraysis,thenumberofthetriangularfacetsthatposethesurfaceofa3Dmodelis,theverticesnumberoftrianglesfacetsisandthefinalnumberofthetriangularfacetsneededtobecalculatedfortheintersectionis.
Becausetheputationofremovingtheno-intersectiontriangularismuchsmallerthanintersectioncalculationbetweentheraysandtrianglefacets,itcanbeignored.Theiterationtimesinray-basedmethodis,theiterationtimesintheimprovedprojectray-basedmethodis.Thus,theratioofputingworkis.Thelargermeansthatthemethodismoreeffective.Thenumberofremovedno-intersectiontriangularfacetsisbymethodbasedondistanceandbymethodbasedonintersectionangle.Theputationofmethodbasedondistanceis,whichislessthanthatofmethodbasedonintersectionangle.FromEq.(5),itcanbeconcludedthatintersectionjudgmentbymethodbasedonintersectionangleismoreplexitythanthatbymethodbasedondistance.Therefore,themethodbasedondistanceisbetter.
Theaboveapproachusessingle-layerspheretoextractfeatures.However,thisapproachignorestheinnerinformationofthemodel,soitisonlysuitableforconvexmodel.Inordertousetheinnerinformationofmodelswhentheapproachisutilizedindealingwithmodelswithothertopologicalstructures,multi-layerspheresapproachisproposed.Thestepsare:(i)limitingthemodelinaball,(ii)dividingtheballintoNlayersaveragely,(iii)emittingtheraysfromcentertosamplingpointsoneachsphere,andcalculatingtheintersectionpointsofraysandthemodel.Ifthereisnosamplingpointbetweenthe(n-1)-thsphereandnthsphere,thenthissamplingpointiseliminatedasthefeaturesofnthlayer,where.
Nowtheexamplesarepresentedtovalidatetheeffectivenessoftheproposedapproach.Thesingle-layersphereisutilizedfirstly,andtheprojectray-basedalgorithmisutilizedtoextractfeatures.ThentheEuclideandistanceisutilizedtoparethesimilaritybetweenmodels,andtheresultsareusedtodrawthePrecision-Recalldiagramtoevaluatetheprecisionoftheretrieval.
ThePrecisionandRecallrepresenttheprecisionratioandrecallratiorespectively,andtheycanbeutilizedtoevaluatetheretrievalresults.Precisionratioistheratioofcorrectmodelsinallretrievedmodels,anditisutilizedtoevaluatetheprecisionofretrievedresults.Precisionratioiscalculatedasthenumberofcorrectmodelsdividedbythenumberofretrievedmodels.Recallratioistheratioofcorrectretrievedmodelsinallmodels,anditisutilizedtoevaluatetheabilitytoretrievethecorrectmodels.Recallratioiscalculatedasthenumberofcorrectretrievedmodelsdividedbythenumberofallmodels.SointhePrecision-Recalldiagram,thecurvewhichisclosertoupper-rigeanstheretrievedresultsarebetter.
Themodelsofbottleandboxareutilizedastestdata,andthenumberofraysis1,024.Intheexperiments,theresultsofdifferentmodelsaredifferent,asshowninFig.8.AccordingtotheresultsinFig.8,thepreciseofboxmodelsislowerthanthatofbottlemodels,andthereasonisthatthetopologicalstructureofboxmodelsismoreplicatedthanthatofbottlemodels.Thereisplentyinnerinformationinboxmodels,sothesingle-layerspherecannotdescribethesemodelsaccurately.
Fig.8Resultsofbottleandboxmodels
Theresultsofboxmodelsarenotverygoodwhenusingsingle-layersphere,sotwo-layerspheresareused,andtheprecisionisimproved.TheresultsareshowninFig.9.
Fig.9Resultsofboxmodels
Accordingtotheexperiments,themulti-layerspheresprojectray-basedapproachcanextractthefeaturesofmodelswiththeplicatedtopologicalstructureeffectively.
TheGearmodels,LflangemodelsandSflangemodelsarealsotakenastestingmodels.Intheexperiments,theraynumbersaresetas1024,andthenthenumbersofspheresareincreasedfrom1to3.Theresultsshowthatretrievedprecisionoftwo-layerspheresmethodismuchbetterthanone-layerspheremethod,whiletheretrievedprecisionofthree-layerspheresmethodisonlylittlebetterthanone-layerspheremethod.Thus,thenumberofspheresshouldbesetareasonablevalue.Theexperimentalsoevaluatesthenumberofrays.Theraynumbersaresetas64,256and1024,andtheresultsshowthattheprecisionincreasesastheincreaseofraynumbers,whiletheimprovementisnotveryobvious.Thus,generally,theraynumberissetas1024,andthetwo-layerspheremethodisutilized.In
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