Screened poisson surface reconstruction

Poisson surface reconstruction creates watertight surfaces from oriented point sets. In this work we extend the technique to explicitly incorporate the points as interpolation constraints. The extension can be interpreted as a generalization of the underlying mathematical framework to a screened Poisson equation. In contrast to other image and geometry processing techniques, the screening term is defined over a sparse set of points rather than over the full domain. We show that these sparse constraints can nonetheless be integrated efficiently. Because the modified linear system retains the same finite-element discretization, the sparsity structure is unchanged, and the system can still be solved using a multigrid approach. Moreover we present several algorithmic improvements that together reduce the time complexity of the solver to linear in the number of points, thereby enabling faster, higher-quality surface reconstructions.

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

[2]  Diego F. Nehab,et al.  Efficiently combining positions and normals for precise 3D geometry , 2005, SIGGRAPH 2005.

[3]  Pierre Alliez,et al.  Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets , 2010, Comput. Graph. Forum.

[4]  Gabriel Taubin,et al.  1 An End-to-End Framework for Evaluating Surface Reconstruction , 2011 .

[5]  Randal C. Burns,et al.  Multilevel streaming for out-of-core surface reconstruction , 2007, Symposium on Geometry Processing.

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

[7]  Michael F. Cohen,et al.  Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems , 2008, ECCV.

[8]  J. Giesen,et al.  Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms , 2004 .

[9]  C. Fletcher.  Computational Galerkin Methods , 1983 .

[10]  Marc Alexa,et al.  Sparse low-degree implicit surfaces with applications to high quality rendering, feature extraction, and smoothing , 2005, SGP '05.

[11]  Jean-Michel Morel,et al.  Farman Institute 3D Point Sets - High Precision 3D Data Sets , 2011, Image Process. Line.

[12]  M. Kazhdan,et al.  Interactive and anisotropic geometry processing using the screened Poisson equation , 2011, SIGGRAPH 2011.

[13]  Pierre Alliez,et al.  Eurographics Symposium on Geometry Processing (2007) Voronoi-based Variational Reconstruction of Unoriented Point Sets , 2022 .

[14]  John Hart,et al.  ACM Transactions on Graphics , 2004, SIGGRAPH 2004.

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

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

[17]  Yutaka Ohtake,et al.  Smoothing of Partition of Unity Implicit Surfaces for Noise Robust Surface Reconstruction , 2009, Comput. Graph. Forum.

[18]  Jean-Michel Morel,et al.  Scale Space Meshing of Raw Data Point Sets , 2011, Comput. Graph. Forum.

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

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

[21]  Steve Oudot,et al.  Provably good sampling and meshing of surfaces , 2005, Graph. Model..

[22]  Bernard Chazelle,et al.  Matching 3D models with shape distributions , 2001, Proceedings International Conference on Shape Modeling and Applications.

[23]  Szymon Rusinkiewicz,et al.  Eurographics Symposium on Geometry Processing (2005) Atomic Volumes for Mesh Completion , 2022 .

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

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

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

[27]  Jean-Philippe Pons,et al.  Robust and Efficient Surface Reconstruction From Range Data , 2009, Comput. Graph. Forum.

[28]  Szymon Rusinkiewicz,et al.  Efficiently combining positions and normals for precise 3D geometry , 2005, ACM Trans. Graph..

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

[30]  Marc Levoy,et al.  QSplat: a multiresolution point rendering system for large meshes , 2000, SIGGRAPH.

[31]  Marc Alexa,et al.  Sparse Low-degree Implicits with Applications to High Quality Rendering, Feature Extraction, and Smoothing , 2005, Symposium on Geometry Processing.

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

[33]  Joachim Giesen,et al.  Delaunay Triangulation Based Surface Reconstruction , 2006 .

[34]  Leif Kobbelt,et al.  Robust reconstruction of watertight 3D models from non-uniformly sampled point clouds without normal information , 2006, SGP '06.

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