On-line CAD Reconstruction with Accumulated Means of Local Geometric Properties

  • Klaus DenkerEmail author
  • Bernd Hamann
  • Georg Umlauf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9213)


Reconstruction of hand-held laser scanner data is used in industry primarily for reverse engineering. Traditionally, scanning and reconstruction are separate steps. The operator of the laser scanner has no feedback from the reconstruction results. On-line reconstruction of the CAD geometry allows for such an immediate feedback.

We propose a method for on-line segmentation and reconstruction of CAD geometry from a stream of point data based on means that are updated on-line. These means are combined to define complex local geometric properties, e.g., to radii and center points of spherical regions. Using means of local scores, planar, cylindrical, and spherical segments are detected and extended robustly with region growing. For the on-line computation of the means we use so-called accumulated means. They allow for on-line insertion and removal of values and merging of means. Our results show that this approach can be performed on-line and is robust to noise. We demonstrate that our method reconstructs spherical, cylindrical, and planar segments on real scan data containing typical errors caused by hand-held laser scanners.


Principal Curvature Unweighted Pair Group Method With Arithmetic Spherical Segment Segment Type Weighted Arithmetic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by DFG grant UM 26/5-1.


  1. 1.
    Agin, G., Binford, T.: Computer description of curved objects. IEEE Trans. Comput. C–25(4), 439–449 (1976)CrossRefGoogle Scholar
  2. 2.
    Benkő, P., Martin, R.R., Várady, T.: Algorithms for reverse engineering boundary representation models. Comput. Aided Des. 33(11), 839–851 (2001)CrossRefGoogle Scholar
  3. 3.
    Benkő, P., Várady, T.: Direct segmentation of smooth, multiple point regions. In: Geometric Modeling and Processing, pp. 169–178. IEEE (2002)Google Scholar
  4. 4.
    Biegelbauer, G., Vincze, M.: Efficient 3D object detection by fitting superquadrics to range image data for robot’s object manipulation. In: International Conference on Robotics and Automation, pp. 1086–1091. IEEE (2007)Google Scholar
  5. 5.
    Bodenmüller, T., Hirzinger, G.: Online surface reconstruction from unorganized 3d-points for the DLR hand-guided scanner system. In: 2nd Symposium on 3D Data Processing, Visualization and Transmission, pp. 285–292 (2004)Google Scholar
  6. 6.
    Boesch, J., Pajarola, R.: Flexible configurable stream processing of point data. In: WSCG 2009, pp. 49–56 (2009)Google Scholar
  7. 7.
    do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Pearson, New York (1976)zbMATHGoogle Scholar
  8. 8.
    Chan, T., Golub, G., Leveque, R.: Algorithms for computing the sample variance: analysis and recommendations. Am. Stat. 37(3), 242–247 (1983)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Denker, K., Hagel, D., Raible, J., Umlauf, G., Hamann, B.: On-line reconstruction of cad geometry. In: International Conference on 3D Vision, pp. 151–158 (2013)Google Scholar
  10. 10.
    Denker, K., Lehner, B., Umlauf, G.: Online triangulation of laser-scan data. In: Garimella, R., (ed.) 17th International Meshing Roundtable, pp. 415–432 (2008)Google Scholar
  11. 11.
    Denker, K., Lehner, B., Umlauf, G.: Real-time triangulation of point streams. Eng. Comput. 27(1), 67–80 (2011)CrossRefGoogle Scholar
  12. 12.
    Gronau, I., Moran, S.: Optimal implementations of upgma and other common clustering algorithms. Inf. Process. Lett. 104(6), 205–210 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Holland, P.W., Welsch, R.E.: Robust regression using iteratively reweighted least-squares. Com. Stat.: Theory Methods A6, 813–827 (1977)CrossRefzbMATHGoogle Scholar
  14. 14.
    Jolliffe, I.: Principal Component Analysis. Springer-Verlag, Heidelberg (2002)zbMATHGoogle Scholar
  15. 15.
    Knuth, D.E.: Seminumerical Algorithms, The Art of Computer Programming, 3rd (edn.), chap. 4.2.2, vol. 2, p. 232. Addison-Wesley, Boston (1998)Google Scholar
  16. 16.
    Ling, R.F.: Comparison of several algorithms for computing sample means and variances. J. Am. Stat. Assoc. 69(348), 859–866 (1974)CrossRefzbMATHGoogle Scholar
  17. 17.
    Page, D., Sun, Y., Koschan, A., Paik, J., Abidi, M.: Normal vector voting: crease detection and curvature estimation on large, noisy meshes. Graph. Models 64, 199–229 (2002)CrossRefzbMATHGoogle Scholar
  18. 18.
    Pajarola, R.: Stream-processing points. In: IEEE Visualization, pp. 239–246 (2005)Google Scholar
  19. 19.
    Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge (2007)Google Scholar
  20. 20.
    Qt Project Hosting: Qt Documentation (2013).
  21. 21.
    Razer: Hydra Motion Sensing Controller (2013).
  22. 22.
    van Reeken, A.J.: Letters to the editor: dealing with Neely’s algorithms. Commun. ACM 11(3), 149–150 (1968)CrossRefGoogle Scholar
  23. 23.
    Schnabel, R., Wahl, R., Klein, R.: Efficient RANSAC for point-cloud shape detection. Comput. Graph. Forum 26(2), 214–226 (2007)CrossRefGoogle Scholar
  24. 24.
    Shamir, A.: A survey on mesh segmentation techniques. Comput. Graph. Forum 27(6), 1539–1556 (2008)CrossRefzbMATHGoogle Scholar
  25. 25.
    Sokal, R.R., Michener, C.D.: A statistical method for evaluating systematic relationships. Univ. Kans. Sci. Bull. 28, 1409–1438 (1958)Google Scholar
  26. 26.
    Vančo, M., Hamann, B., Brunnett, G.: Surface reconstruction from unorganized point data with quadrics. Comput. Graph. Forum 27(6), 1593–1606 (2008)CrossRefzbMATHGoogle Scholar
  27. 27.
    Várady, T.: Reverse engineering of geometric models - an introduction. Comp. Aided Des. 29(4), 255–268 (1997)CrossRefGoogle Scholar
  28. 28.
    Welford, B.P.: Note on a method for calculating corrected sums of squares and products. Technometrics 4(3), 419–420 (1962)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Wu, J., Kobbelt, L.: Structure recovery via hybrid variational surface approximation. Comput. Graph. Forum 24(3), 277–284 (2005)CrossRefGoogle Scholar
  30. 30.
    Yamazaki, I., Natarajan, V., Bai, Z., Hamann, B.: Segmenting point-sampled surfaces. Vis. Comput. 26(12), 1421–1433 (2010)CrossRefGoogle Scholar
  31. 31.
    Zhong, S.: Efficient online spherical \(k\)-means clustering. In: Proceedings of 2005 IEEE International Joint Conference on Neural Networks, vol. 5, pp. 3180–3185 (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Optical SystemsUniversity of Applied Science ConstanceKonstanzGermany
  2. 2.Institute for Data Analysis and Visualization (IDAV), Department of Computer ScienceUniversity of CaliforniaDavisUSA

Personalised recommendations