Implicit Surface Reconstruction with an Analogy of Polar Field Model

  • Yuxu Lin
  • Chun Chen
  • Mingli Song
  • Jiajun Bu
  • Zicheng Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5414)


Implicit surface reconstruction has been a challenging work for decades. In this paper, motivated by the concept of classic physical polar field model and off-set points strategy, we present a new approach, called Field Fitting. In this approach, we express a 3D surface as an equipotential surface of scalar polar field which is produced by a number of paired field generating primitives, then a surface reconstruction process is cast as a primitives localization process, and finally, we solve this problem with a greedy method. Experimental results demonstrate that the proposed method outperforms the previous by providing better surface reconstruction results.


Surface fitting reconstruction polar field implicit surface Field Fitting 


  1. 1.
    Bloomenthal, J., Bajaj, C.: Introduction to Implicit Surfaces. Morgan Kaufmann, San Francisco (1997)zbMATHGoogle Scholar
  2. 2.
    Dierckx, P.: Curve and Surface Fitting with Splines. Oxford University Press, Oxford (1993)zbMATHGoogle Scholar
  3. 3.
    Floater, M., Hormann, K.: Surface Parameterization: a Tutorial and Survey. Advances In Multiresolution For Geometric Modelling (2005)Google Scholar
  4. 4.
    Blane, M., Lei, Z., Çivi, H., Cooper, D.: The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 298–313 (2000)Google Scholar
  5. 5.
    Carr, J., Beatson, R., Cherrie, J., Mitchell, T., Fright, W., McCallum, B., Evans, T.: Reconstruction and representation of 3D objects with radial basis functions. In: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp. 67–76 (2001)Google Scholar
  6. 6.
    Carr, J., Beatson, R., McCallum, B., Fright, W., McLennan, T., Mitchell, T.: Smooth surface reconstruction from noisy range data. ACM GRAPHITE 3, 119–126 (2003)CrossRefzbMATHGoogle Scholar
  7. 7.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proceedings of the 19th annual conference on Computer graphics and interactive techniques, pp. 71–78 (1992)Google Scholar
  8. 8.
    Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.: Point set surfaces. In: Proceedings of the conference on Visualization 2001, pp. 21–28 (2001)Google Scholar
  9. 9.
    Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T.: Computing and Rendering Point Set Surfaces. Computing 9(1), 3–15 (2003)Google Scholar
  10. 10.
    Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.: Multi-level partition of unity implicits. In: International Conference on Computer Graphics and Interactive Techniques, pp. 463–470 (2003)Google Scholar
  11. 11.
    Kazhdan, M., Bolitho, M., Hoppe, H.: Poisson Surface Reconstruction. Indicator 1(1) (2006)Google Scholar
  12. 12.
    Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C++. Cambridge Univ. Press, Cambridge (2002)zbMATHGoogle Scholar
  13. 13.
    Mitra, N., Nguyen, A.: Estimating surface normals in noisy point cloud data. In: Proceedings of the nineteenth annual symposium on Computational geometry, pp. 322–328 (2003)Google Scholar
  14. 14.
    Ohtake, Y., Belyaev, A., Seidel, H.: A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions. In: Shape Modeling International 2003, pp. 153–161 (2003)Google Scholar
  15. 15.
    Tobor, I., Reuter, P., Schlick, C.: Multi-scale reconstruction of implicit surfaces with attributes from large unorganized point sets. In: Proceedings of Shape Modeling Applications, pp. 19–30 (2004)Google Scholar
  16. 16.
    Bloomenthal, J.: An implicit surface polygonizer. Graphics Gems IV 349 (1994)Google Scholar
  17. 17.
    Hart, J.: Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer 12(10), 527–545 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yuxu Lin
    • 1
  • Chun Chen
    • 1
  • Mingli Song
    • 1
  • Jiajun Bu
    • 1
  • Zicheng Liu
    • 2
  1. 1.College of Computer ScienceZhejiang UniversityChina
  2. 2.Microsoft Research RedmondUSA

Personalised recommendations