简介:Isometric3Dshapepartialmatchinghasattractedagreatamountofinterest,withaplethoraofapplicationsrangingfromshaperecognitiontotexturemapping.Inthispaper,weproposeanovelisometric3DshapepartialmatchingalgorithmusingthegeodesicdiskLaplacespectrum(GD-DNA).Ittransformsthepartialmatchingproblemintothegeodesicdiskmatchingproblem.Firstly,thelargestenclosedgeodesicdiskextractedfromthepartialshapeismatchedwithgeodesicdisksfromthefullshapebytheLaplacespectrumofthegeodesicdisk.Secondly,GeneralizedMulti-DimensionalScalingalgorithm(GMDS)andEuclideanembeddingareconductedtoestablishfinalpointcorrespondencesbetweenthepartialandthefullshapeusingthematchedgeodesicdiskpair.TheproposedGD-DNAisdiscriminativeformatchinggeodesicdisks,anditcanwellsolvetheanchorpointselectionprobleminchallengingpartialshapematchingtasks.ExperimentalresultsontheShapeRetrievalContest2016(SHREC'16)benchmarkvalidatetheproposedmethod,andcomparisonswithisometricpartialmatchingalgorithmsintheliteratureshowthatourmethodhasahigherprecision.
简介:研究了非线性随机动力系统所对应的Fokker-Planck-kolmogorov(FPK)方程.讨论了微分方程的可朗克(Crank)一尼考尔逊(Nicolson)型隐式有限差分格式以及微分的四阶中心差分格式,将两者相结合,得到FPK方程的四阶中心C-N隐式格式差分解,并与FPK方程的精确解进行了比较.数值结果表明,该方法具有良好的稳定性,且可以解决其他方法在概率密度峰值处偏小,而在尾部处较大等缺点.