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Home > Archive>Volume 15, Issue zk, 2004 >230-238
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A Neighborhood Centroid Constrained Fairing Algorithm for Point Clouds
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    Abstract:

    A fairing algorithm with centroid constraints ofneighborhood is presented for point-sampled geometry．By optimizing a local function based on the centroid constraints of neighborhood, local smoothing is achieved without surface reconstruction．This method overcomes the problems of extreme shrinkage and extreme convergence arisen from Laplacian smoofaing operator so that it achieves little distortion．The experimental results verify that it is stable，fast and easy-to-use．

    Reference
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    [2] Linderberg T.Scale-Space Theory in Computer Vision.Norwell:Kluwer Academic Publishers,1994.
    [3] Pauly M.Point primitives for interactive modeling and processing of 3D geometry[Ph.D.Thesis].Zfirich:ETH Zurich,2003.
    [4] Taubin G:A signal processing approach to fair surface design.In:Cook R,ed.Proe.of ACM SIGGRAPH’95.New York:ACM Press,1995.351～358.
    [5] Desbrun M,Meyer M,Schroder P,Barr AH.Implicit fairing of irregular meshes using diffusion and curvature flow.In:Rockwood A,ed.Proc.of ACM SIGGRAPH’99.New York:ACM Press.1999.317～324.
    [6] Vollmer J,Mencl R,Mfiller H.Improved laplacian smoothing of noisy surface meshes.In:Brunder P,Scopigno R,eds.Proc.of EuroGraphies’99.Milan:Eurographics Association and Blackwell Publishers,1999,18(3).
    [7] Guskov I,Sweldens W,Schr6der P.Multiresolution signal processing for meshes.In:Rockwood A,ed.Proc.of ACM SIGGRAPH’99.New York:ACM Press,1999.371～380.
    [8] Kobbelt LP.Discrete fairing and variational subdivision for freeform surface design.The Visual Computer,2000,16(3/4):142～150.
    [9] Peng J,Strela V,Zorin D.A Simple Algorithm for Surface Denoising.In:Ertl T,Joy KI,Varshney A,eds.Proc.of IEEE Visualization 2001,Los Alamitos,CA:IEEE Computer Society Press,2001.107-112. ‘
    [10] Jones TR,Durand F,Desbmn M.Non-Iterative,feature-preserving mesh smoothing.In:Hart JC ed.Proc.of ACM SIGGRAPH 2003.New York:ACM Press,2003.943～949.
    [11] Fleishman S,Drori I,Cohen-Or D.Bilateral mesh denoising.In:Hart JC,ed.Proc.of ACM SIGGRAPH 2003.New York:ACM Press,2003.950～953.
    [12] Liu XG.Three dimensional geometry compression[Ph.D.Thesis].Hangzhou:Zhejiang University,2001(in Chinese with English abstract).
    [13] Pauly M,Kobbelt LP,Gross M.Multiresolution modeling of point-sampled geometry.Technical Report,CS#379,Zfirich:ETH Ziirich,2002.
    [14] Sagan H.Introduction to the Calculus ofVariations.New York:Dover Publications,1969.
    [15] Pauly M,Gross M,and Kobbelt LP.Efficient Simplification of Point-sampled Surfaces.In:Proc.of IEEE Visualization 2002.Los Alamitos:IEEE Computer Society Press,2002.163～170. 附中文参考文献:
    [12] 刘新国.三维几何压缩[博士学位论文].杭州:浙江大学,2001. 附录: 定义D1:矩阵M=(mij)m×n称为可约的,若存在置换阵P,使得PAPT=(MM22),其中M11,M22为方阵.定理Tl:设M=(mij)m×n弱对角占优并且不可约,则M非奇.证明:在式(4)中,对称矩阵A的每一行都满足: 如果矩阵A的每一行上式等号成立,则根据式(8)矩阵A每一行和均为O,此时A奇异.反过来若上式对A的某一行等 号不成立,则A是弱对角占优矩阵,同时A不可约.由定理Tl,此时矩阵A非奇.另一方面,A可约存在Nbhd(pi)的非空真子集J,有:对.由于f∈Nbhd(p),对W∈Nbhd(pt),有％=％≠0,因此A不可约.综上所述,A奇异当且仅当A的每一行的和均为0.
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杨振羽,郑文庭,彭群生.基于邻域重心约束的点云模型光顺算法.软件学报,2004,15(zk):230-238

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