Curvature-aware adaptive re-sampling for point-sampled geometry

With the emergence of large-scale point-sampled geometry acquired by high-resolution 3D scanning devices, it has become increasingly important to develop efficient algorithms for processing such models which have abundant geometric details and complex topology in general. As a preprocessing step, surface simplification is important and necessary for the subsequent operations and geometric processing. Owing to adaptive mean-shift clustering scheme, a curvature-aware adaptive re-sampling method is proposed for point-sampled geometry simplification. The generated sampling points are non-uniformly distributed and can account for the local geometric feature in a curvature aware manner, i.e. in the simplified model the sampling points are dense in the high curvature regions, and sparse in the low curvature regions. The proposed method has been implemented and demonstrated by several examples.

[1]  Markus H. Gross,et al.  Shape modeling with point-sampled geometry , 2003, ACM Trans. Graph..

[2]  Konrad Polthier,et al.  Anisotropic smoothing of point sets, , 2005, Comput. Aided Geom. Des..

[3]  Guido Brunnett,et al.  Geometric Modeling for Scientific Visualization , 2010 .

[4]  Ayellet Tal,et al.  Hierarchical mesh decomposition using fuzzy clustering and cuts , 2003, ACM Trans. Graph..

[5]  N. Dodgson,et al.  Intrinsic point cloud simplification , 2004 .

[6]  Derek Nowrouzezahrai,et al.  Robust statistical estimation of curvature on discretized surfaces , 2007, Symposium on Geometry Processing.

[7]  Chunxia Xiao,et al.  Differentials-Based Segmentation and Parameterization for Point-Sampled Surfaces , 2007, Journal of Computer Science and Technology.

[8]  Marc Levoy,et al.  The digital Michelangelo project: 3D scanning of large statues , 2000, SIGGRAPH.

[9]  Marc Alexa,et al.  Computing and Rendering Point Set Surfaces , 2003, IEEE Trans. Vis. Comput. Graph..

[10]  Tamal K. Dey,et al.  Decimating samples for mesh simplification , 2001, CCCG.

[11]  Dereck S. Meek,et al.  On surface normal and Gaussian curvature approximations given data sampled from a smooth surface , 2000, Comput. Aided Geom. Des..

[12]  Chi-Keung Tang,et al.  Robust estimation of adaptive tensors of curvature by tensor voting , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Ilan Shimshoni,et al.  Mean shift based clustering in high dimensions: a texture classification example , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[15]  Szymon Rusinkiewicz,et al.  Estimating curvatures and their derivatives on triangle meshes , 2004, Proceedings. 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004..

[16]  Hans-Peter Seidel,et al.  Feature sensitive mesh segmentation with mean shift , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[17]  Lars Linsen,et al.  Point cloud representation , 2001 .

[18]  Jarek Rossignac,et al.  Solid modeling , 1994, IEEE Computer Graphics and Applications.

[19]  Xiaoping Qian,et al.  Eurographics Symposium on Point-based Graphics (2007) Direct Computing of Surface Curvatures for Point-set Surfaces , 2022 .

[20]  Meenakshisundaram Gopi On sampling and reconstructing surfaces with boundaries , 2002, CCCG.

[21]  John C. Hart,et al.  Using particles to sample and control more complex implicit surfaces , 2005, SIGGRAPH Courses.

[22]  Marc Alexa,et al.  On Normals and Projection Operators for Surfaces Defined by Point Sets , 2004, PBG.

[23]  Markus H. Gross,et al.  Efficient simplification of point-sampled surfaces , 2002, IEEE Visualization, 2002. VIS 2002..

[24]  Ilan Shimshoni,et al.  Estimating the principal curvatures and the darboux frame from real 3-D range data , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[25]  Gabriel Taubin,et al.  Estimating the tensor of curvature of a surface from a polyhedral approximation , 1995, Proceedings of IEEE International Conference on Computer Vision.

[26]  Leonidas J. Guibas,et al.  Estimating surface normals in noisy point cloud data , 2004, Int. J. Comput. Geom. Appl..

[27]  Cindy Grimm,et al.  Estimating Curvature on Triangular Meshes , 2006, Int. J. Shape Model..

[28]  Mario Costa Sousa,et al.  Eurographics Symposium on Point-based Graphics (2007) Sampling Point-set Implicits , 2022 .

[29]  Renato Pajarola,et al.  Confetti: object-space point blending and splatting , 2004, IEEE Transactions on Visualization and Computer Graphics.

[30]  Paul S. Heckbert,et al.  Using particles to sample and control implicit surfaces , 1994, SIGGRAPH Courses.

[31]  Marc Pouget,et al.  Estimating differential quantities using polynomial fitting of osculating jets , 2003, Comput. Aided Geom. Des..

[32]  Amitabh Varshney,et al.  Statistical Point Geometry , 2003, Symposium on Geometry Processing.

[33]  Sunghee Choi,et al.  The power crust , 2001, SMA '01.

[34]  N. Dodgson,et al.  A new point cloud simplification algorithm , 2003 .

[35]  Kenneth L. Clarkson,et al.  Building triangulations using ε-nets , 2006, STOC '06.

[36]  Ilan Shimshoni,et al.  Estimating the principal curvatures and the Darboux frame from real 3D range data , 2002, Proceedings. First International Symposium on 3D Data Processing Visualization and Transmission.

[37]  Leif Kobbelt,et al.  Optimized Sub‐Sampling of Point Sets for Surface Splatting , 2004, Comput. Graph. Forum.

[38]  Tim Weyrich,et al.  Post-processing of Scanned 3D Surface Data , 2004, PBG.

[39]  Wojciech Jarosz,et al.  Using particles to sample and control more complex implicit surfaces , 2002, Proceedings SMI. Shape Modeling International 2002.

[40]  D. Levin,et al.  Mesh-Independent Surface Interpolation , 2004 .

[41]  Tamal K. Dey,et al.  Shape Dimension and Approximation from Samples , 2002, SODA '02.

[42]  Dorin Comaniciu,et al.  Mean shift analysis and applications , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[43]  N. Amenta,et al.  Defining point-set surfaces , 2004, SIGGRAPH 2004.

[44]  Michael Garland,et al.  Hierarchical face clustering on polygonal surfaces , 2001, I3D '01.

[45]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[46]  Greg Turk,et al.  Re-tiling polygonal surfaces , 1992, SIGGRAPH.

[47]  Philip Shilane,et al.  Stratified Point Sampling of 3D Models , 2004, PBG.

[48]  Victoria Interrante,et al.  A novel cubic-order algorithm for approximating principal direction vectors , 2004, TOGS.

[49]  Paolo Cignoni,et al.  Metro: Measuring Error on Simplified Surfaces , 1998, Comput. Graph. Forum.

[50]  Matthias Zwicker,et al.  Pointshop 3D: an interactive system for point-based surface editing , 2002, SIGGRAPH.