Surface Reconstruction through Poisson Disk Sampling

This paper intends to generate the approximate Voronoi diagram in the geodesic metric for some unbiased samples selected from original points. The mesh model of seeds is then constructed on basis of the Voronoi diagram. Rather than constructing the Voronoi diagram for all original points, the proposed strategy is to run around the obstacle that the geodesic distances among neighboring points are sensitive to nearest neighbor definition. It is obvious that the reconstructed model is the level of detail of original points. Hence, our main motivation is to deal with the redundant scattered points. In implementation, Poisson disk sampling is taken to select seeds and helps to produce the Voronoi diagram. Adaptive reconstructions can be achieved by slightly changing the uniform strategy in selecting seeds. Behaviors of this method are investigated and accuracy evaluations are done. Experimental results show the proposed method is reliable and effective.

[1]  Martin Reimers,et al.  Meshless parameterization and surface reconstruction , 2001, Comput. Aided Geom. Des..

[2]  Meenakshisundaram Gopi,et al.  Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation , 2000, Comput. Graph. Forum.

[3]  Pierre Alliez,et al.  Computational geometry algorithms library , 2008, SIGGRAPH '08.

[4]  Xin Li,et al.  Poisson disk sampling in geodesic metric for DEM simplification , 2013, Int. J. Appl. Earth Obs. Geoinformation.

[5]  Laurent D. Cohen,et al.  Geodesic Remeshing Using Front Propagation , 2003, International Journal of Computer Vision.

[6]  Neil A. Dodgson,et al.  Fast Marching farthest point sampling , 2003, Eurographics.

[7]  Martin Isenburg,et al.  Centroidal Voronoi diagrams for isotropic surface remeshing , 2005, Graph. Model..

[8]  Ryan Schmidt,et al.  Consensus meshing , 2012, Comput. Graph..

[9]  Der-Chen Chang,et al.  Hopf fibration: Geodesics and distances , 2010, 1009.4789.

[10]  A. Ardeshir Goshtasby,et al.  A Curvature-Adaptive Implicit Surface Reconstruction for Irregularly Spaced Points , 2012, IEEE Transactions on Visualization and Computer Graphics.

[11]  Craig Gotsman,et al.  Explicit Surface Remeshing , 2003, Symposium on Geometry Processing.

[12]  Sunil Arya,et al.  ANN: library for approximate nearest neighbor searching , 1998 .

[13]  Li-Yi Wei,et al.  Parallel Poisson disk sampling with spectrum analysis on surfaces , 2010, ACM Trans. Graph..

[14]  Herbert Edelsbrunner,et al.  Computational Topology - an Introduction , 2009 .

[15]  Tamal K. Dey,et al.  Curve and Surface Reconstruction , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[16]  Marshall W. Bern,et al.  Surface Reconstruction by Voronoi Filtering , 1998, SCG '98.

[17]  Randal C. Burns,et al.  Parallel Poisson Surface Reconstruction , 2009, ISVC.

[18]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[19]  David Eppstein,et al.  The Crust and the beta-Skeleton: Combinatorial Curve Reconstruction , 1998, Graph. Model. Image Process..

[20]  Jean-Daniel Boissonnat,et al.  Effective computational geometry for curves and surfaces , 2006 .

[21]  Robert L. Cook,et al.  Stochastic sampling in computer graphics , 1988, TOGS.

[22]  Michela Spagnuolo,et al.  Shape Analysis and Structuring , 2008 .

[23]  Marco Attene,et al.  Recent Advances in Remeshing of Surfaces , 2008, Shape Analysis and Structuring.

[24]  D. Cohen-Or,et al.  Robust moving least-squares fitting with sharp features , 2005, ACM Trans. Graph..

[25]  Hans-Peter Seidel,et al.  An integrating approach to meshing scattered point data , 2005, SPM '05.

[26]  Tony DeRose,et al.  Surface reconstruction from unorganized points , 1992, SIGGRAPH.

[27]  Luiz Velho,et al.  Geodesic paths on triangular meshes , 2004, Proceedings. 17th Brazilian Symposium on Computer Graphics and Image Processing.

[28]  Sunghee Choi,et al.  The power crust, unions of balls, and the medial axis transform , 2001, Comput. Geom..

[29]  John Hart,et al.  ACM Transactions on Graphics: Editorial , 2003, SIGGRAPH 2003.

[30]  Hugues Hoppe,et al.  Progressive meshes , 1996, SIGGRAPH.

[31]  Stefan Jeschke,et al.  Dart Throwing on Surfaces , 2009, Comput. Graph. Forum.

[32]  Ares Lagae,et al.  A Comparison of Methods for Generating Poisson Disk Distributions , 2008, Comput. Graph. Forum.

[33]  Michael M. Kazhdan,et al.  Poisson surface reconstruction , 2006, SGP '06.

[34]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[35]  Jacek Raczkowski,et al.  Modeling the Motion of Dense Smoke in the Wind Field , 2000, Comput. Graph. Forum.