Poisson Surface Reconstruction with Envelope Constraints

Reconstructing surfaces from scanned 3D points has been an important research area for several decades. One common approach that has proven efficient and robust to noise is implicit surface reconstruction, i.e. fitting to the points a 3D scalar function (such as an indicator function or signed‐distance field) and then extracting an isosurface. Though many techniques fall within this category, existing methods either impose no boundary constraints or impose Dirichlet/Neumann conditions on the surface of a bounding box containing the scanned data.

[1]  Pieter Abbeel,et al.  BigBIRD: A large-scale 3D database of object instances , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[2]  Otfried Cheong,et al.  The reflex-free hull , 2001, CCCG.

[3]  William L. Briggs,et al.  A multigrid tutorial , 1987 .

[4]  T SilvaClaudio,et al.  A Survey of Surface Reconstruction from Point Clouds , 2017 .

[5]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[6]  M. Magnor,et al.  Free-Viewpoint Video from Depth Cameras , 2006 .

[7]  Chandrajit L. Bajaj,et al.  Automatic reconstruction of surfaces and scalar fields from 3D scans , 1995, SIGGRAPH.

[8]  James F. O'Brien,et al.  Interpolating and approximating implicit surfaces from polygon soup , 2004, SIGGRAPH Courses.

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

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

[11]  M. Goesele,et al.  Floating scale surface reconstruction , 2014, ACM Trans. Graph..

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

[13]  Olga Sorkine-Hornung,et al.  Robust inside-outside segmentation using generalized winding numbers , 2013, ACM Trans. Graph..

[14]  Josiah Manson,et al.  Streaming Surface Reconstruction Using Wavelets , 2008, Comput. Graph. Forum.

[15]  Alec Jacobson,et al.  Thingi10K: A Dataset of 10, 000 3D-Printing Models , 2016, ArXiv.

[16]  William L. Briggs,et al.  A multigrid tutorial, Second Edition , 2000 .

[17]  Michael M. Kazhdan,et al.  An Adaptive Multi‐Grid Solver for Applications in Computer Graphics , 2019, Comput. Graph. Forum.

[18]  Gabriel Taubin,et al.  The ball-pivoting algorithm for surface reconstruction , 1999, IEEE Transactions on Visualization and Computer Graphics.

[19]  V. Rokhlin,et al.  The fast multipole method (FMM) for electromagnetic scattering problems , 1992 .

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

[21]  Marshall W. Bern,et al.  A new Voronoi-based surface reconstruction algorithm , 1998, SIGGRAPH.

[22]  Zuoqiang Shi,et al.  Surface Reconstruction Based on the Modified Gauss Formula , 2018, ACM Trans. Graph..

[23]  Demetri Terzopoulos,et al.  Sampling and reconstruction with adaptive meshes , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[24]  Hans-Peter Seidel,et al.  Multi-level partition of unity implicits , 2003, ACM Trans. Graph..

[25]  Jean-Daniel Boissonnat,et al.  Geometric structures for three-dimensional shape representation , 1984, TOGS.

[26]  Michael M. Kazhdan,et al.  Screened poisson surface reconstruction , 2013, TOGS.

[27]  Ulrich Reif,et al.  Weighted Extended B-Spline Approximation of Dirichlet Problems , 2001, SIAM J. Numer. Anal..

[28]  E LorensenWilliam,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987 .

[29]  Pierre Alliez,et al.  A Survey of Surface Reconstruction from Point Clouds , 2017, Comput. Graph. Forum.

[30]  HoppeHugues,et al.  Surface Reconstruction from Unorganized Points , 1992 .

[31]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[32]  S. McCormick,et al.  A multigrid tutorial (2nd ed.) , 2000 .

[33]  James F. O'Brien,et al.  Spectral surface reconstruction from noisy point clouds , 2004, SGP '04.

[34]  Gérard G. Medioni,et al.  Description of Complex Objects from Multiple Range Images Using an Inflating Balloon Model , 1995, Comput. Vis. Image Underst..

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

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

[37]  Marc Levoy,et al.  A volumetric method for building complex models from range images , 1996, SIGGRAPH.

[38]  Gabriel Taubin,et al.  SSD: Smooth Signed Distance Surface Reconstruction , 2011, Comput. Graph. Forum.

[39]  Daniel Cohen-Or,et al.  Cone carving for surface reconstruction , 2010, ACM Trans. Graph..