Tomographic surface reconstruction from point cloud

Inspired by computed tomography (CT), this paper presents a novel surface reconstruction algorithm, tomographic surface reconstruction, to reconstruct a surface mesh from a point cloud equipped with oriented normals. In the process of scanning a real object using an X-ray CT system, it generates a sinogram consisting of projection images that are maps of X-ray transmission lengths, and then, a tomogram (CT volume) is reconstructed from the sinogram. A hole-free surface mesh is then easily obtained by polygonizing an isosurface. To adopt this CT paradigm to surface reconstruction from a point cloud, only a scheme to generate a sinogram from a point cloud is required. The value of a sinogram for surface reconstruction can be defined as the sum of the distances between the intersecting points of a ray and the underlying surface, which are defined as the maxima of the point density. While ordinary CT scanning uses projection directions which share a single rotation axis, tomographic surface reconstruction adopts randomly selected projection directions and successfully improved the reconstruction robustness. By applying an iterative CT reconstruction to the sinogram, the algorithm generates a tomogram whose boundary between the foreground and background approximates the surface of the object. The effectiveness for a point cloud with a lack of sampling and outliers is demonstrated from experimental results. Graphical abstractDisplay Omitted HighlightsA novel approach for surface reconstruction using a CT-reconstruction algorithm.Enhancing robustness to compute transmission-length for a point cloud.Robustness over noise and outliers is demonstrated.

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

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

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

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

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

[6]  Jiang Hsieh,et al.  Computed Tomography: Principles, Design, Artifacts, and Recent Advances, Fourth Edition , 2022 .

[7]  Matthew J. Sottile,et al.  Curve and surface reconstruction: algorithms with mathematical analysis by Tamal K. Dey Cambridge University Press , 2010, SIGA.

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

[9]  H. Seidel,et al.  Multi-level partition of unity implicits , 2003 .

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

[11]  Larry D. Hostetler,et al.  The estimation of the gradient of a density function, with applications in pattern recognition , 1975, IEEE Trans. Inf. Theory.

[12]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[13]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

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

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

[16]  Gabriel Taubin,et al.  A benchmark for surface reconstruction , 2013, TOGS.

[17]  H. Malcolm Hudson,et al.  Accelerated image reconstruction using ordered subsets of projection data , 1994, IEEE Trans. Medical Imaging.

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

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

[20]  Daniel Cohen-Or,et al.  Consolidation of unorganized point clouds for surface reconstruction , 2009, ACM Trans. Graph..

[21]  Tamal K. Dey,et al.  Tight cocone: a water-tight surface reconstructor , 2003, SM '03.

[22]  Tamal K. Dey,et al.  Provable surface reconstruction from noisy samples , 2006, Comput. Geom..

[23]  Pierre Alliez,et al.  State of the Art in Surface Reconstruction from Point Clouds , 2014, Eurographics.

[24]  Tao Ju,et al.  Dual contouring of hermite data , 2002, ACM Trans. Graph..

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

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

[27]  Marcus A. Magnor,et al.  Adaptive grid optical tomography , 2006, Graph. Model..

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

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

[30]  Andrew W. Fitzgibbon,et al.  KinectFusion: Real-time dense surface mapping and tracking , 2011, 2011 10th IEEE International Symposium on Mixed and Augmented Reality.