Efficientdatavisualizationtechniquesarecriticalformanyscientificapplications.CentroidalVoronoitessellation(CVT)basedalgorithmsofferaconvenientvehicleforperformingimageanalysis,segmentationandcompressionwhileallowingtooptimizeretainedimagequalitywithrespecttoagivenmetric.InexperimentalsciencewithdatacountsfollowingPoissondistributions,severalCVT-baseddatatessellationalgorithmshavebeenrecentlydeveloped.Althoughtheysurpasstheirpredecessorsinrobustnessandqualityofreconstructeddata,timeconsumptionremainstobeanissueduetoheavyutilizationoftheslowlyconvergingLloyditeration.Thispaperdiscussesonepossibleapproachtoacceleratingdatavisualizationalgorithms.ItreliesonamultidimensionalgeneralizationoftheoptimizationbasedmultilevelalgorithmforthenumericalcomputationoftheCVTsintroducedin[1],wherearigorousproofofitsuniformconvergencehasbeenpresentedin1-dimensionalsetting.Themultidimensionalimplementationemploysbarycentriccoordinatebasedinterpolationandmaximalindependentsetcoarseningprocedures.Itisshownthatwhencoupledwithbinaccretionalgorithmaccountingforthediscretenatureofthedata,thealgorithmoutperformsLloyd-basedschemesandpreservesuniformconvergencewithrespecttotheproblemsize.Althoughnumericaldemonstrationsprovidedarelimitedtospectroscopydataanalysis,themethodhasacontext-independentsetupandcanpotentiallydeliversignificantspeeduptootherscientificandengineeringapplications.
