简介:Inthispaper,itisprovedthat,given3controlpointsA,BandC,ifthecamera'sopticalcenterOliesononeofthethreeplanesperpendiculartotheplaneABCandgoingthroughoneofthethreealtitudesofthetriangleABC,andadditionallyitsprojectionontheplaneABCiswithinthecircumscribedcircleofthetriangle,thatis,Oiswithintheso-called'dangercylinder',thenthecorrespondingP3Pproblem{O,(ABC)}musthave4positivesolutions.Thisresultispurelygeometrical,andmoreinstructive.Itcanbringsomenewinsightintoabetterunderstandingofmultiple-solutionprobleminthePnPproblem,andcouldbeusedassometheoreticalguidetoarrangecontrolpointsinrealapplications.
简介:Isometric3Dshapepartialmatchinghasattractedagreatamountofinterest,withaplethoraofapplicationsrangingfromshaperecognitiontotexturemapping.Inthispaper,weproposeanovelisometric3DshapepartialmatchingalgorithmusingthegeodesicdiskLaplacespectrum(GD-DNA).Ittransformsthepartialmatchingproblemintothegeodesicdiskmatchingproblem.Firstly,thelargestenclosedgeodesicdiskextractedfromthepartialshapeismatchedwithgeodesicdisksfromthefullshapebytheLaplacespectrumofthegeodesicdisk.Secondly,GeneralizedMulti-DimensionalScalingalgorithm(GMDS)andEuclideanembeddingareconductedtoestablishfinalpointcorrespondencesbetweenthepartialandthefullshapeusingthematchedgeodesicdiskpair.TheproposedGD-DNAisdiscriminativeformatchinggeodesicdisks,anditcanwellsolvetheanchorpointselectionprobleminchallengingpartialshapematchingtasks.ExperimentalresultsontheShapeRetrievalContest2016(SHREC'16)benchmarkvalidatetheproposedmethod,andcomparisonswithisometricpartialmatchingalgorithmsintheliteratureshowthatourmethodhasahigherprecision.