Detection of Planar Regions in Volume Data for Topology Optimization

  • Ulrich Bauer
  • Konrad Polthier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4975)


We propose a method to identify planar regions in volume data using a specialized version of the discrete Radon transform operating on a structured or unstructured grid. The algorithm uses an efficient discretization scheme for the parameter space to obtain a running time of \(\mathcal O(N (T\log T))\), where T is the number of cells and N is the number of plane normals in the discretized parameter space.

We apply our algorithm in an industrial setting and perform experiments with real-world data generated by topology optimization algorithms, where the planar regions represent portions of a mechanical part that can be built using steel plate.


Discrete Radon transform Hough transform Plane detection Topology optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bendsøe, M.: Topology Optimization: Theory, Methods, and Applications. Springer, Heidelberg (2003)Google Scholar
  2. 2.
    Stolpe, M.: On Models and Methods for Global Optimization of Structural Topology. KTH, Mathematics, Stockholm (2003)Google Scholar
  3. 3.
    Sigmund, O.: A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization 21(2), 120–127 (2001)CrossRefGoogle Scholar
  4. 4.
    Ben-Tal, A., Bendsøe, M.: A New Method for Optimal Truss Topology Design. SIAM Journal on Optimization 3, 322 (1993)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    de Klerk, E., Roos, C.,T.T.: Semi-definite problems in truss topology optimization. Technical Report Report 95–128, Faculty of Technical Mathematics and Informatics, Delft, Netherlands (1995)Google Scholar
  6. 6.
    Radon, J.: Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte Sächsische Akademie der Wissenschaften, Leipzig, Mathematisch-Physikalische Klasse 69, 262–277 (1917)Google Scholar
  7. 7.
    Hough, P.: Method and Means for Recognizing Complex Patterns, United States Patent US 3,069,654, 18.12.2002 (1962)Google Scholar
  8. 8.
    Duda, R.O., Hart, P.E.: Use of the Hough transformation to detect lines and curves in pictures. Commun. ACM 15(1), 11–15 (1972)CrossRefGoogle Scholar
  9. 9.
    Sarti, A., Tubaro, S.: Detection and characterisation of planar fractures using a 3d hough transform. Signal Processing 82(9), 1269–1282 (2002)CrossRefzbMATHGoogle Scholar
  10. 10.
    Vosselman, G., Dijkman, S.: 3D building model reconstruction from point clouds and ground plans. International Archives of Photogrammetry and Remote Sensing 34(3/W4), 37–43 (2001)Google Scholar
  11. 11.
    Kurdi, F.T., Landes, T., Grussenmeyer, P.: Hough-Transform and Extended RANSAC Algorithms for Automatic Detection of 3D Building Roof Planes from Lidar Data. In: Proceedings of the ISPRS Workshop on Laser Scanning, pp. 407–412 (2007)Google Scholar
  12. 12.
    Peternell, M., Steiner, T.: Reconstruction of piecewise planar objects from point clouds. Computer-Aided Design 36(4), 333–342 (2004)CrossRefGoogle Scholar
  13. 13.
    Paralambros, P.Y., Chirehdast, M.: An integrated environment for structural configuration design. Journal of Engineering Design 1, 73–96 (1990)CrossRefGoogle Scholar
  14. 14.
    Hornlein, H., Kocvara, M., Werner, R.: Material optimization: bridging the gap between conceptual and preliminary design. Aerospace Science and Technology 5(8), 541–554 (2001)CrossRefGoogle Scholar
  15. 15.
    Katanforoush, A., Shahshahani, M.: Distributing Points on the Sphere, I. Experimental Mathematics 12(2), 199–209 (2003)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ulrich Bauer
    • 1
  • Konrad Polthier
    • 1
  1. 1.FU BerlinBerlinGermany

Personalised recommendations