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一种基于正则参数化的降维细分算法(英文) Introduction Dimensionalityreductionandsubdivisionaretwoimportanttechniquesinthefieldofcomputergraphics.Whiledimensionalityreductionaimstoreducethenumberofdimensionsinadataset,subdivisionseekstoincreasetheresolutionofageometricmodel.Despitetheirdifferences,thesetechniquesshareacommongoal:tosimplifytherepresentationofcomplexdataorgeometrieswhilepreservingtheiressentialfeatures.Thispaperpresentsanovelmethodthatcombinesbothtechniquesusingregularizedparameterizationtoachieveefficientandeffectivesubdivision-baseddimensionalityreduction. Background Traditionalapproachestodimensionalityreduction,suchasprincipalcomponentanalysisandlineardiscriminantanalysis,havelimitationsindealingwithnon-linearandhigh-dimensionaldata.Incontrast,subdivision-basedtechniqueshaveproventobeeffectiveinhandlingcomplexgeometricmodels,suchasthoseencounteredincomputer-aideddesignanddigitalentertainment.Thesetechniquesiterativelyrefineagivenmeshtocreateahigherresolutionrepresentationoftheoriginalmodel.However,suchrefinementcanalsoleadtoanexplosionofdata,makingitchallengingtohandleandprocesstheresultingmesh. Recentresearchhassoughttointegratesubdivisionwithdimensionalityreductiontechniques.Oneapproachistoapplydimensionalityreductionbeforesubdivisiontocreatealower-dimensionalembeddingoftheoriginaldatathatcanbemoreefficientlyrefined.However,thequalityofthefinalresultcanbelimitedbytheinitialembedding,whichmaynotcaptureallrelevantinformation. Anotherapproachistoapplysubdivisionbeforedimensionalityreduction,whichcanresultinahigh-dimensionaldatasetthatischallengingtoprocess.However,thisapproachhasthepotentialtocapturemorerelevantfeaturesbyrefiningthegeometryinadata-drivenmanner. Approach Ourmethodaddressesthelimitationsofbothpriorapproachesbyusingaregularizedparameterizationtointegratesubdivisionanddimensionalityreduction.Specifically,weuseamethodknownasharmonicparameterization,whichdefinesamapfromthesurfaceofthemeshtoaplanardomainwhilepreservingthedistanceandanglebetweenadjacentvertice