A novel 3D mesh compression using mesh segmentation with multiple principal plane analysis(14)

i=1

11

19

12

1

2

Z’H

y’

x’

Fig.10.Theprojectedregionisonatwo-dimensionalspacebyrotatingtheregion

Hoftheprincipalplanewiththeaxisz:(a)thewithaligningthenormalvectorn

H)originalmeshinthex–y–zspace

and(b)theprojectedmeshinthex –y –z (n

space.

i|isthenum-where|M|isthenumberofverticesinMand|Ri∩R

berofverticeswhicharebothwithinthesegmentedregionRifor

iforthenoise-addedmeshmodel.ThevaluetheoriginalmeshandR

ofSPishighwhenthesegmentedregionsofanoise-addedmesharealmostthesameasthoseoftheoriginalmesh.InthecaseofFig.12,thevalueofSPachieves99%.Thus,theproposedsegmenta-tionalgorithmisrobustinresistingnoise.

Thecurrentsegmentationprocedureproducesthecorrectseg-mentationofthemodel.Thenumberofregionssegmentedfromacomplexmeshmodelaffectsprecisecompactrepresentation.Fig.13showsthatvaryingthenumberofsegments(kmax)usedintheseg-mentationprocedureleadstoadaptivemeshsmoothingwithsimul-taneoussharpeningofsurfacecreasesatdifferentgeometricscales.Fig.14showsdistributingreconstructionerrorsofFig.13(a)usingsegmentedregionstoapproximatetheoriginalinputmesh.Accord-ingly,theproposedmeshsegmentationprocedureprovidesaccuratecompactrepresentationtoapproximatetheinputmesh.Accordingto(15),wecancalculatethereconstructionerrorforaninputmesh.Fig.15showsothersegmentationresultsfordifferentmeshmodels,andTable1listsreconstructionerrorsusingthesegmentedregionstoapproximatetheinputmodels.

Fig.11.Examplesof3Dtriangularmodelsusedformeasurements:(a)“nefertiti”;(b)“body”;(c)“tiger”;(d)“bunny”;(e)“triceratops.”

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