The Visual Computer

, Volume 25, Issue 5–7, pp 391–399 | Cite as

Creating MPU implicit surfaces from unoriented point sets with orientation inference

  • Yi-Ling ChenEmail author
  • Shang-Hong Lai
Original Article


In this paper, we extend the MPU implicits algorithm to deal with unoriented point sets while preserving its desirable properties, such as sharp feature preservation. An orientation inference algorithm is introduced to orientate the local implicit patches by solving a graph labeling problem through energy minimization. Sign consistency between local functions is exploited to infer the globally consistent orientation. To precisely model the features, we employ the affinity propagation clustering algorithm to identify the local surface patches composing the features by considering orientation consistency between data points. Sharp features can then be accurately reconstructed by performing piecewise smooth surface fitting. Experimental results are shown to demonstrate the performance of the proposed algorithm.


Implicit surfaces Orientation inference Sharp features 


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  1. 1.
    Alliez, P., Cohen-Steiner, D., Tong, Y., Desbrun, M.: Voronoi-based variational reconstruction for unoriented point sets. In: Proceedings of Symposium on Geometry Processing, pp. 39–48 (2007) Google Scholar
  2. 2.
    Amenta, N., Bern, M., Kamvysselis, M.: A new Voronoi-based surface reconstruction algorithm. In: ACM SIGGRAPH, pp. 415–420 (1998) Google Scholar
  3. 3.
    Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R.: Reconstruction and representation of 3d objects with radial basis functions. In: ACM SIGGRAPH, pp. 67–76 (2001) Google Scholar
  4. 4.
    Chen, Y.L., Lai, S.H., Lee, T.Y.: Generalized MPU implicits using belief propagation. In: Proceedings of 3-D Digital Imaging and Modeling, pp. 400–407 (2007) Google Scholar
  5. 5.
    Dinh, H.Q., Turk, G., Slabaugh, G.: Reconstructing surfaces by volumetric regularization using radial basis functions. IEEE Trans. Pattern Anal. Mach. Intell. 24(10), 1358–1371 (2002) CrossRefGoogle Scholar
  6. 6.
    Dey, T.K., Sun, J.: An adaptive MLS surface for reconstruction with guarantees. In: Proceedings of Symposium on Geometry Processing (2005) Google Scholar
  7. 7.
    Fleishman, S., Cohen-Or, D., Silva, C.T.: Robust moving least-squares fitting with sharp features. In: ACM SIGGRAPH (2005) Google Scholar
  8. 8.
    Franke, R., Nielson, G.: Smooth interpolation of large sets of scattered data. Int. J. Numer. Methods Eng. 15, 1691–1704 (1980) zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Frey, B.J., Dueck, D.: Clustering by passing messages between data points. Science 315(5814), 972–976 (2007) CrossRefMathSciNetGoogle Scholar
  10. 10.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: ACM SIGGRAPH, pp. 71–78 (1992) Google Scholar
  11. 11.
    Ju, T., Losasso, F., Schaefer, S., Warren, J.: Dual contouring of Hermite data. In: ACM SIGGRAPH, pp. 339–346 (2002) Google Scholar
  12. 12.
    Kazhdan, M., Bolitho, M., Hoppe, H.: Poisson surface reconstruction. In: Proceedings of Symposium on Geometry Processing (2006) Google Scholar
  13. 13.
    Kobbelt, L.P., Botsch, M., Schwanecke, U., Seidel, H.P.: Feature sensitive surface extraction from volume data. In: ACM SIGGRAPH (2001) Google Scholar
  14. 14.
    Kolluri, R.: Provably good moving least squares. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (2005) Google Scholar
  15. 15.
    Lipman, Y., Cohen-Or, D., Levin, D.: Data-dependent MLS for faithful surface approximation. In: Proceedings Symposium on Geometry Processing, pp. 59–67 (2007) Google Scholar
  16. 16.
    Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3d surface construction algorithm. In: Computer Graphics (Proceedings of SIGGRAPH 87), vol. 21, pp. 163–169 (1987) Google Scholar
  17. 17.
    Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.P.: Multi-level partition of unity implicits. In: ACM SIGGRAPH (2003) Google Scholar
  18. 18.
    Ohtake, Y., Belyaev, A., Alexa, M.: Sparse low-degree implicit surfaces with applications to high quality rendering, feature extraction, and smoothing. In: Symposium on Geometry Processing (2005) Google Scholar
  19. 19.
    Ohtake, Y., Belyaev, A.G., Seidel, H.P.: Sparse surface reconstruction with adaptive partition of unity and radial basis functions. Graph. Models 68(1), 15–24 (2006) zbMATHCrossRefGoogle Scholar
  20. 20.
    Ohtake, Y., Belyaev, A., Seidel, H.P.: Ridge-valley lines on meshes via implicit surface fitting. In: ACM SIGGRAPH (2004) Google Scholar
  21. 21.
    Pauly, M., Keiser, R., Gross, M.: Multi-scale feature extraction on point-sampled surfaces. In: Proceedings of Eurographics, vol. 22 (2003) Google Scholar
  22. 22.
    Stylianou, G., Farin, G.: Crest lines for surface segmentation and flattening. IEEE Trans. Vis. Comput. Graph. 10(5), 536–544 (2004) CrossRefGoogle Scholar
  23. 23.
    Taubin, G.: An improved algorithm for algebraic curve and surface fitting. In: Proceedings of International Conference on Computer Vision (ICCV), pp. 658–665 (1993) Google Scholar
  24. 24.
    Tobor, I., Reuter, P., Schlick, C.: Reconstructing multi-scale variational partition of unity implicit surfaces with attributes. Graph. Models 68(1), 25–41 (2006) zbMATHCrossRefGoogle Scholar
  25. 25.
    Turk, G., O’Brien, J.F.: Modelling with implicit surfaces that interpolate. ACM Trans. Graph. 21(4), 855–873 (2002) CrossRefGoogle Scholar
  26. 26.
    Weiss, Y., Freeman, W.T.: On the optimality of solutions of the max-product belief propagation algorithm in arbitrary graphs. IEEE Trans. Inf. Theory 47(2), 723–735 (2001) CrossRefMathSciNetGoogle Scholar
  27. 27.
    Xie, H., Wang, J., Hua, J., Qin, H., Kaufman, A.: Piecewise c1 continuous surface reconstruction of noisy point clouds via local implicit quadric regression. In: IEEE Visualization, pp. 91–98 (2003) Google Scholar
  28. 28.
    Xie, H., McDonnel, K.T., Qin, H.: Surface reconstruction of noisy and defective data sets. In: IEEE Visualization, pp. 259–266 (2004) Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan

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