Hierarchical Structure Recovery of Point‐Sampled Surfaces

We focus on the class of ‘regular’ models defined by Várady et al. for reverse engineering purposes. Given a 3D surface  represented through a dense set of points, we present a novel algorithm that converts  to a hierarchical representation . In , the surface is encoded through patches of various shape and size, which form a hierarchical atlas. If  belongs to the class of regular models, then  captures the most significant features of  at all the levels of detail. In this case, we show that  can be exploited to interactively select regions of interest on  and intuitively re‐design the model. Furthermore,  intrinsically encodes a hierarchy of useful ‘segmentations’ of . We present a simple though efficient approach to extract and optimize such segmentations, and we show how they can be used to approximate the input point sets through idealized manifold meshes.

[1]  Marco Attene,et al.  Sharpen&Bend: recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling , 2005, IEEE Transactions on Visualization and Computer Graphics.

[2]  Marco Attene,et al.  ReMESH: An Interactive Environment to Edit and Repair Triangle Meshes , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

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

[4]  Marco Attene,et al.  Hierarchical Convex Approximation of 3D Shapes for Fast Region Selection , 2008, Comput. Graph. Forum.

[5]  Leif Kobbelt,et al.  Structure Recovery via Hybrid Variational Surface Approximation , 2005, Comput. Graph. Forum.

[6]  Tamal K. Dey,et al.  Shape Segmentation and Matching with Flow Discretization , 2003, WADS.

[7]  Marc Alexa,et al.  Approximating and Intersecting Surfaces from Points , 2003, Symposium on Geometry Processing.

[8]  Dong-Ming Yan,et al.  Quadric Surface Extraction by Variational Shape Approximation , 2006, GMP.

[9]  Micha Sharir,et al.  Filling gaps in the boundary of a polyhedron , 1995, Comput. Aided Geom. Des..

[10]  Franc Solina,et al.  A Direct Recovery of Superquadric Models in Range Images Using Recover-and-Select Paradigm , 1994, ECCV.

[11]  Bernard Chazelle,et al.  Strategies for polyhedral surface decomposition: an experimental study , 1995, SCG '95.

[12]  Marc Alexa,et al.  Point-based computer graphics , 2004, SIGGRAPH '04.

[13]  Franc Solina,et al.  Superquadrics for Segmenting and Modeling Range Data , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  François Goulette,et al.  Extracting Cylinders in Full 3D Data Using a Random Sampling Method and the Gaussian Image , 2001, VMV.

[15]  Ariel Shamir,et al.  Segmentation and Shape Extraction of 3D Boundary Meshes , 2006, Eurographics.

[16]  Marco Attene,et al.  Hierarchical mesh segmentation based on fitting primitives , 2006, The Visual Computer.

[17]  Ioannis Pratikakis,et al.  3D Mesh Segmentation Methodologies for CAD applications , 2007 .

[18]  K. Shimada,et al.  Face clustering of a large-scale CAD model for surface mesh generation , 2001, Comput. Aided Des..

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

[20]  Hans-Peter Seidel,et al.  Mesh segmentation driven by Gaussian curvature , 2005, The Visual Computer.

[21]  Ayellet Tal,et al.  Polyhedral surface decomposition with applications , 2002, Comput. Graph..

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

[23]  Ralph R. Martin,et al.  Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation , 1998, ECCV.

[24]  Guido Brunnett,et al.  Direct Segmentation of Algebraic Models for Reverse Engineering , 2003, Computing.

[25]  Yiying Tong,et al.  Discrete differential forms for computational modeling , 2005, SIGGRAPH Courses.

[26]  Sunil Arya,et al.  An optimal algorithm for approximate nearest neighbor searching fixed dimensions , 1998, JACM.

[27]  Marc Alexa,et al.  Point set surfaces , 2001, Proceedings Visualization, 2001. VIS '01..

[28]  Hao Zhang,et al.  Segmentation of 3D meshes through spectral clustering , 2004, 12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings..

[29]  M. Gross,et al.  Algebraic point set surfaces , 2007, SIGGRAPH 2007.

[30]  J. Rossignac,et al.  Plumber: a method for a multi-scale decomposition of 3D shapes into tubular primitives and bodies , 2004, SM '04.

[31]  Leonidas J. Guibas,et al.  Shape segmentation using local slippage analysis , 2004, SGP '04.

[32]  Zhiyong Huang,et al.  Decomposing polygon meshes by means of critical points , 2004, 10th International Multimedia Modelling Conference, 2004. Proceedings..

[33]  Reinhard Klein,et al.  Efficient RANSAC for Point‐Cloud Shape Detection , 2007, Comput. Graph. Forum.

[34]  Jarek Rossignac,et al.  Blowing Bubbles for Multi-Scale Analysis and Decomposition of Triangle Meshes , 2003, Algorithmica.

[35]  Ali Shokoufandeh,et al.  Local Feature Extraction Using Scale-Space Decomposition , 2004 .

[36]  Douglas Kelker,et al.  A mathematical model for orientation data from macroscopic elliptical conical folds , 1987 .

[37]  Tony DeRose,et al.  Piecewise smooth surface reconstruction , 1994, SIGGRAPH.

[38]  Ralph R. Martin,et al.  Reverse engineering of geometric models - an introduction , 1997, Comput. Aided Des..

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

[40]  Hans-Peter Seidel,et al.  Mesh scissoring with minima rule and part salience , 2005, Comput. Aided Geom. Des..

[41]  Giuseppe Patanè,et al.  Para‐Graph: Graph‐Based Parameterization of Triangle Meshes with Arbitrary Genus , 2004, Comput. Graph. Forum.

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

[43]  Marco Attene,et al.  Mesh Segmentation - A Comparative Study , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[44]  Konstantin Mischaikow,et al.  Feature-based surface parameterization and texture mapping , 2005, TOGS.

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

[46]  Szymon Rusinkiewicz,et al.  Modeling by example , 2004, SIGGRAPH 2004.

[47]  Marc Alexa,et al.  Progressive point set surfaces , 2003, TOGS.

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

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

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

[51]  Bernd Hamann,et al.  Segmenting Point Sets , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[52]  Vaughan R. Pratt,et al.  Direct least-squares fitting of algebraic surfaces , 1987, SIGGRAPH.

[53]  Mathieu Desbrun,et al.  Variational shape approximation , 2004, SIGGRAPH 2004.

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

[55]  Tamal K. Dey,et al.  An Adaptive MLS Surface for Reconstruction with Guarantees , 2022 .

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