“A Benchmark for Surface Reconstruction” by Berger, Levine, Nonato and Taubin

  • ©Matthew Berger, Joshua A. Levine, Luis Gustavo Nonato, and Gabriel Taubin

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Title:

    A Benchmark for Surface Reconstruction

Session/Category Title: Surface Reconstruction

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Abstract:


    We present a benchmark for the evaluation and comparison of algorithms which reconstruct a surface from point cloud data. Although a substantial amount of effort has been dedicated to the problem of surface reconstruction, a comprehensive means of evaluating this class of algorithms is noticeably absent. We propose a simple pipeline for measuring surface reconstruction algorithms, consisting of three main phases: surface modeling, sampling, and evaluation. We use implicit surfaces for modeling shapes which are capable of representing details of varying size and sharp features. From these implicit surfaces, we produce point clouds by synthetically generating range scans which resemble realistic scan data produced by an optical triangulation scanner. We validate our synthetic sampling scheme by comparing against scan data produced by a commercial optical laser scanner, where we scan a 3D-printed version of the original surface. Last, we perform evaluation by comparing the output reconstructed surface to a dense uniformly distributed sampling of the implicit surface. We decompose our benchmark into two distinct sets of experiments. The first set of experiments measures reconstruction against point clouds of complex shapes sampled under a wide variety of conditions. Although these experiments are quite useful for comparison, they lack a fine-grain analysis. To complement this, the second set of experiments measures specific properties of surface reconstruction, in terms of sampling characteristics and surface features. Together, these experiments depict a detailed examination of the state of surface reconstruction algorithms.

References:


    1. Abbasinejad, F., Kil, Y., Sharf, A., and Amenta, N. 2009. Rotating scans for systematic error removal. Comput. Graph. Forum 28, 1319–1326.
    2. Abramowitz, M. and Stegun, I. 1964. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Vol. 55, Dover Publications.
    3. Adamson, A. and Alexa, M. 2003. Approximating and intersecting surfaces from points. In Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. Eurographics Association, 230–239.
    4. Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., and Silva, C. 2003. Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. Graph. 9, 3–15.
    5. Alliez, P., Cohen-Steiner, D., Tong, Y., ad Desbrun, M. 2007. Voronoi-Based variational reconstruction of unoriented point sets. In Proceedings of the Symposium on Geometry Processing. Eurographics Association, 39–48.
    6. Amenta, N. and Bern, M. 1999. Surface reconstruction by Voronoi filtering. Discr. Comput. Geom. 22, 4, 481–504.
    7. Amenta, N., Choi, S., Dey, T. K., and Leekha, N. 2002. A simple algorithm for homeomorphic surface reconstruction. Int. J. Comput. Geom. Appl. 12, 1–2, 125–141.
    8. Amenta, N., Choi, S., and Kolluri, R. 2001. The power crust. In Proceedings of the ACM Symposium on Solid Modeling and Applications. ACM Press, New York, 249–266.
    9. Baribeau, R. and Rioux, M. 1991. Influence of speckle on laser range finders. Appl. Opt. 30, 20, 2873–2878.
    10. Boissonnat, J.-D. and Cazals, F. 2002. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Comput. Geom. 22, 1–3, 185–203.
    11. Bouguet, J. 2010. Camera calibration toolbox for Matlab. http://www. vision.caltech.edu/bouguetj/calib_doc
    12. Brown, B. and Rusinkiewicz, S. 2007. Global non-rigid alignment of 3-D scans. ACM Trans. Graph. 26, 3, 21:1–21:10.
    13. Cao, J., Tagliasacchi, A., Olson, M., Zhang, H., and Su, Z. 2010. Point cloud skeletons via Laplacian based contraction. In Proceedings of the International Conference on Shape Modeling (SMI’10). IEEE, 187–197.
    14. Cazals, F. and Giesen, J. 2006. Delaunay triangulation based surface reconstruction. In Effective Computational Geometry for Curves and Surfaces, J.-D. Boissonnat and M. Teillaud, Eds., Springer, 231–276.
    15. Cignoni, P., Montani, C., and Scopigno, R. 1998. A comparison of mesh simplification algorithms. Comput. Graph. 22, 1, 37–54.
    16. Curless, B. and Levoy, M. 1995. Better optical triangulation through spacetime analysis. In Proceedings of the 5th International Conference on Computer Vision. IEEE, 987–994.
    17. 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.
    18. Dey, T., Woo, H., and Zhao, W. 2003. Approximate medial axis for cad models. In Proceedings of the 8th ACM Symposium on Solid Modeling and Applications. ACM Press, New York, 280–285.
    19. Dey, T. K. 2007. Curve and Surface Reconstruction: Algorithms with Mathematical Analysis. Cambridge University Press.
    20. Dey, T. K., Li, G., and Sun, J. 2005. Normal estimation for point clouds: A comparison study for a Voronoi based method. In Proceedings of the Symposium on Point-Based Graphics. Eurographics Association, 39–46.
    21. Fleishman, S., Cohen-Or, D., and Silva, C. T. 2005. Robust moving least-squares fitting with sharp features. ACM Trans. Graph. 24, 3, 544–552.
    22. Frueh, C., Jain, S., and Zakhor, A. 2005. Data processing algorithms for generating textured 3D building façade meshes from laser scans and camera images. Int. J. Comput. Vis. 61, 2, 159–184.
    23. Funkhouser, T., Shin, H., Toler-Franklin, C., Castaneda, A., Brown, B., Dobkin, D., Rusikiewicz, S., and Weyrich, T. 2011. Learning how to match fresco fragments. J. Comput. Cult. Herit. 4, 2, 7.
    24. Garland, M. and Heckbert, P. S. 1997. Surface simplification using quadric error metrics. In Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’97). ACM Press/Addison-Wesley Publishing, New York, 209–216.
    25. Guennebaud, G. and Gross, M. 2007. Algebraic point set surfaces. ACM Trans. Graph. 26, 3, 23:1–23:10.
    26. Hildebrandt, K., Polthier, K., and Wardetzky, M. 2006. On the convergence of metric and geometric properties of polyhedral surfaces. Geometriae Dedicata I23, 1, 89–112.
    27. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., and Stuetzle, W. 1992. Surface reconstruction from unorganized points. In Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’92). ACM Press, New York, 71–78.
    28. Kazhdan, M. 2005. Reconstruction of solid models from oriented point sets. In Proceedings of the Symposium on Geometry Processing. Eurographics Association, 73–82.
    29. Kazhdan, M., Bolitho, M., and Hoppe, H. 2006. Poisson surface reconstruction. In Proceedings of the Symposium on Geometry Processing. Eurographics Association, 61–70.
    30. Kolluri, R. 2005. Provably good moving least squares. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’05). 1008–1017.
    31. Levoy, M., Pulli, K., Curless, B., Rusinkiewicz, S., Koller, D., Pereira, L., Ginzton, M., Anderson, S., Davis, J., Ginsberg, J., et al. 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). ACM Press/Addison-Wesley Publishing, 131–144.
    32. Lipman, Y. and Levin, D. 2010. Derivation and analysis of Green coordinates. Comput. Methods Funct. Theory 10, 1, 167–188.
    33. Manson, J., Petrova, G., and Schaefer, S. 2008. Streaming surface reconstruction using wavelets. Comput. Graph. Forum 27, 1411–1420.
    34. Meyer, M., Desbrun, M., Schroder, P., and Barr, A. 2002. Discrete differential-geometry operators for triangulated 2-manifolds. Vis. Math. 3, 7, 34–57.
    35. Meyer, M., Kirby, R., and Whitaker, R. 2007. Topology, accuracy, and quality of isosurface meshes using dynamic particles. IEEE Trans. Vis. Comput. Graph. 13, 6, 1704–1711.
    36. Mitra, N. J. and Nguyen, A. 2003. Estimating surface normal in noisy point cloud data. In Proceedings of the 19th Annual Symposium on Computational Geometry (SCG’03). ACM Press, New York, 322–328.
    37. Nagai, Y., Ohtake, Y., and Suzuki, H. 2009. Smoothing of partition of unity implicit surfaces for noise robust surface reconstruction. Comput. Graph. Forum 28, 1339–1348.
    38. Nan, L., Sharf, A., Zhang, H., Cohen-Or, D., and Chen, B. 2010. SmartBoxes for interactive urban reconstruction. In ACM SIGGRAPH Papers. ACM Press, New York, 1–10.
    39. NextEngine. 2011. NextEngine 3d laser scanner. http://www.nextengine. com
    40. Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., and Seidel, H. 2003. Multi-Level partition of unity implicits. ACM Trans. Graph. 22, 3, 463–470.
    41. Ohtake, Y., Belyaev, A., and Seidel, H. 2005a. An integrating approach to meshing scattered point data. In Proceedings of the ACM Symposium on Solid and Physical Modeling. ACM Press, New York, 61–69.
    42. Ohtake, Y., Belyaev, A. G., and Seidel, H.-P. 2005b. 3D scattered data interpolation and approximation with multilevel compactly supported rbfs. Graph. Models 67, 3, 150–165.
    43. Regli, W. and Gaines, D. 1997. A repository for design, process planning and assembly. Comput.-Aid. Des. 29, 12, 895–905.
    44. Scharstein, D. and Szeliski, R. 2002. A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. Int. J. Comput. Vis. 47, 1, 7–42.
    45. Seitz, S., Curless, B., Diebel, J., Scharstein, D., and Szeliski, R. 2006. A comparison and evaluation of multi-view stereo reconstruction algorithms. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol. 1, IEEE Computer Society, 519–528.
    46. Shalom, S., Shamir, A., Zhang, H., and Cohen-Or, D. 2010. Cone carving for surface reconstruction. ACM Trans. Graph. 29, 6, 150:1–150:10.
    47. Shapeways. 2011. Shapeways. http://www.shapeways.com
    48. Shen, C., O’Brien, J., and Shewchuk, J. 2004. Interpolating and approximating implicit surfaces from polygon soup. ACM Trans. Graph. 23, 3, 896–904.
    49. Süßmuth, J., Meyer, Q., and Greiner, G. 2010. Surface reconstruction based on hierarchical floating radial basis functions. Comput. Graph. Forum 29, 1854–1864.
    50. Tagliasacchi, A., Zhang, H., and Cohen-Or, D. 2009. Curve skeleton extraction from incomplete point cloud. ACM Trans. Graph. 28, 3, 71:1–71:9.
    51. ter Haar, F., Cignoni, P., Min, P., and Veltkamp, R. 2005. A comparison of systems and tools for 3D scanning. In 3D Digital Imaging and Modeling: Applications of Heritage, Industry, Medicine and Land Workshop (Session P.12).
    52. Vlasic, D., Peers, P., Baran, I., Debevec, P., Popovic, J., Rusinkiewicz, S., and Matusik, W. 2009. Dynamic shape capture using multi-view photometric stereo. ACM Trans. Graph. 28, 5, 174:1–174:11.

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