“Screened Poisson-Surface Reconstruction” by Kazhdan and Hoppe

  • ©Michael Kazhdan and Hugues Hoppe

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Title:

    Screened Poisson-Surface Reconstruction

Session/Category Title: Surface Reconstruction

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Abstract:


    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.

References:


    1. Alliez, P., Cohen-Steiner, D., Tong, Y., and Desbrun, M. 2007. Voronoi-based variational reconstruction of unoriented point sets. In Proceedings of the Symposium on Geometry Processing. 39–48.
    2. Amenta, N., Choi, S., and Kolluri, R. 2001. Power crust. In Proceedings of the ACM Symposium on Solid Modeling and Applications. 249–260.
    3. Bajaj, C., Bernardini, F., and Xu, G. 1995. Automatic reconstruction of surfaces and scalar fields from 3D scans. In Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’95). 109–118.
    4. Berger, M., Levine, J., Nonato, L., Taubin, G., and Silva, C. 2011. An end-to-end framework for evaluating surface reconstruction. Tech. rep. UUSCI-2011-001, SCI Institute, University of Utah.
    5. Bhat, P., Curless, B., Cohen, M., and Zitnick, L. 2008. Fourier analysis of the 2D screened Poisson equation for gradient domain problems. In Proceedings of the European Conference on Computer Vision. 114–128.
    6. Boissonnat, J. and Oudot, S. 2005. Provably good sampling and meshing of surfaces. Graph. Models 67, 5, 405–451.
    7. Bolitho, M., Kazhdan, M., Burns, R., and Hoppe, H. 2007. Multilevel streaming for out-of-core surface reconstruction. In Proceedings of the Symposium on Geometry Processing. 69–78.
    8. Bolitho, M., Kazhdan, M., Burns, R., and Hoppe, H. 2009. Parallel Poisson surface reconstruction. In Proceedings of the International Symposium on Visual Computing.
    9. Calakli, F. and Taubin, G. 2011. SSD: Smooth signed distance surface reconstruction. Comput. Graph. Forum 30, 7.
    10. Carr, J., Beatson, R., Cherrie, H., Mitchell, T., Fright, W., McCallum, B., and Evans, T. 2001. Reconstruction and representation of 3D objects with radial basis functions. In Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’01). 67–76.
    11. Cazals, F. and Giesen, J. 2006. Delaunay triangulation based surface reconstruction: Ideas and algorithms. In Effective Computational Geometry for Curves and Surfaces, Springer, 231–273.
    12. Chuang, M. and Kazhdan, M. 2011. Interactive and anisotropic geometry processing using the screened Poisson equation. ACM Trans. Graph. 30, 4.
    13. Cignoni, P. and Scopigno, R. 1998. Metro: Measuring error on simplified surfaces. Comput. Graph. Forum 17, 2.
    14. Curless, B. and Levoy, M. 1996. A volumetric method for building complex models from range images. In Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’96). 303–312.
    15. Digne, J., Audfray, N., Lartigue, C., Mehdi-Souzani, C., and Morel, J.-M. 2011a. Farman institute 3D point sets—high precision 3D data sets. http://www.ipol.im/pub/art/2011/dalmm_ps/
    16. Digne, J., Morel, J.-M., Souzani, C.-M., and Lartigue, C. 2011b. Scale space meshing of raw data point sets. Comput. Graph. Forum 30, 6.
    17. Fletcher, C. 1984. Computational Galerkin Methods. Springer.
    18. Hoppe, H., Derose, T., Duchamp, T., McDonald, J., and Stuetzle, W. 1992. Surface reconstruction from unorganized points. In Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’92). 71–78.
    19. Hornung, A. and Kobbelt, L. 2006. Robust reconstruction of watertight 3D models from non-uniformly sampled point clouds without normal information. In Proceedings of the Symposium on Geometry Processing. 41–50.
    20. Kazhdan, M., Bolitho, M., and Hoppe, H. 2006. Poisson surface reconstruction. In Proceedings of the Symposium on Geometry Processing. 61–70.
    21. Kolluri, R., Shewchuk, J., and O’Brien, J. 2004. Spectral surface reconstruction from noise point clouds. In Proceedings of the Symposium on Geometry Processing. 11–21.
    22. Labatut, P., Pons, J.-P., and Keriven, R. 2009. Robust and efficient surface reconstruction from range data. Comput. Graph. Forum 28, 8, 2275–2290.
    23. Levoy, M., Pulli, K., Curless, B., Rusinkiewicz, S., Koller, D., Pereira, L., Ginzton, M., Anderson, S., Davis, J., Ginsberg, J., Shade, J., and Fulk, D. 2000. The digital Michelangelo project: 3D scanning of large statues. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’00). 131–144.
    24. Manson, J., Petrova, G., and Schaefer, S. 2008. Streaming surface reconstruction using wavelets. In Proceedings of the Symposium on Geometry Processing. 1411–1420.
    25. Mullen, P., De Goes, F., Desbrun, M., Cohen-Steiner, D., and Alliez, P. 2010. Signing the unsigned: robust surface reconstruction from raw pointsets. In Proceedings of the Symposium on Geometry Processing. 1733–1741.
    26. Nagai, Y., Ohtake, Y., and Suzuki, H. 2009. Smoothing of partition of unity implicit surfaces for noise robust surface reconstruction. Comput. Graph. Forum 28, 5, 1339–1348.
    27. Nehab, D., Rusinkiewicz, S., Davis, J., and Ramamoorthi, R. 2005. Efficiently combining positions and normals for precise 3D geometry. ACM Trans. Graph. 24, 3, 536–543.
    28. Ohtake, Y., Belyaev, A., and Alexa, M. 2005. Sparse low-degree implicits with applications to high quality rendering, feature extraction, and smoothing. In Proceedings of the Symposium on Geometry Processing. 149–158.
    29. Osada, R., Funkhouser, T., Chazelle, B., and Dobkin, D. 2001. Matching 3D models with shape distributions. In Proceedings of the International Conference on Shape Modeling and Applications (SMI’01). 154–166.
    30. Podolak, J. and Rusinkiewicz, S. 2005. Atomic volumes for mesh completion. In Proceedings of the Symposium on Geometry Processing.
    31. Rusinkiewicz, S. and Levoy, M. 2000. QSplat: A multiresolution point rendering system for large meshes. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’00). 343–352.

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