A novel 3D mesh compression using mesh segmentation with multiple principal plane analysis(13)

274S.-C.Chengetal./PatternRecognition43(2010)267--279

vertexforthenextruntoscanunvisitedvertices.InS,vertex13hastwoneighboringvertices14and19.Again,wescanthevertices(4,3,2,1)fromtheedgebetween14and13totheedgebetween19and13(Fig.8(c))andoutputtheinternalconnectivity–geometrydescriptioncode T,4 T,3 T,2 T,1

whereT=1indicatesthattheaccompanyinginformationforeachbracedpartisavertexindexwhosecoordinateshavebeencoded.Inthiscase,(4,3,2,1)areboundaryverticescodedintheaboveboundarycodingprocedure.Afterthestep,vertex13willberemovedfromSandvertex14isthenextseed.FurtherstepsintheconquestareshowninFig.8(d)–(i).

Toreconstructtheinputmesh,thereconstructionalgorithmini-tiallyrestorestheboundary(0–12)usingtheboundarydescriptioncode(Fig.9(a)).Nowfromthefirstinternalconnectivity–geometrydescriptioncodedefinedin(19),thealgorithmrestorestheinternalnodes(13,19,16,17,14)(Fig.9(b)),resultinginsettingthevertex13asthenewseednodeandtheedgesfrom14to13andfrom19to13formthetwosidesofthenextrestorationrun.Thesuccessive

reconstructionoffanscontinuesuntiltheentiremeshisrecon-structedasshowninFig.9(c)–(i).

Theinternalconnectivity–geometrycodingalgorithmvisitstheinputregionverticesonitsprincipalplane.Foreachvertex,thedepthvalueshouldbeaddedintothecodingstreamtorestoreitsoriginalcoordinates.Theprojectedregionisona2DspaceifwerotatetheregionbyaligningtheaxiszwiththenormalvectoroftheprincipalplaneasshowninFig.10.5.Experimentalresults

Toevaluatetheeffectivenessoftheproposedsegmentation-basedcompression,thecurrentstudyimplementsa3Dmeshmodelcompressionsystemforgeometricandconnectiveencod-ing/reconstructionofmeshesonaPCwithPentiumIV1.8GHzCPUrunningtheWindowsXPoperatingsystem.Theexperimentsusedasetof3Dmeshmodels(Fig.11)forperformancemeasurementsthatarefreelyavailableontheInternet.

Thisinvestigationfirsttestedeffectivenessoftheproposedmeshsegmentationalgorithmusingthehybridofk-meansclusteringandthemultipleprincipalplanesanalysis.Fig.12showsthesegmenta-tionresultofthisapproachappliedtoanoisysimple“triceratops”modelwith90%verticesmovedalongthesurfacenormals.GiventhesegmentationresultoftheoriginalmeshmodelMasthegroundtruth,wemightderiveasimplecriterionSPtoverifyrobustnessoftheproposedmeshsegmentationalgorithm.SPisdefinedas

k1 i||Ri∩RSP=H

z

y

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9

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6

51413

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