Advertisement

Fast and Accurate 3D Edge Detection for Surface Reconstruction

  • Christian Bähnisch
  • Peer Stelldinger
  • Ullrich Köthe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5748)

Abstract

Although edge detection is a well investigated topic, 3D edge detectors mostly lack either accuracy or speed. We will show, how to build a highly accurate subvoxel edge detector, which is fast enough for practical applications. In contrast to other approaches we use a spline interpolation in order to have an efficient approximation of the theoretically ideal sinc interpolator. We give theoretical bounds for the accuracy and show experimentally that our approach reaches these bounds while the often-used subpixel-accurate parabola fit leads to much higher edge displacements.

Keywords

Edge Detection Line Search Point Spread Function Spline Interpolation Edge Point 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brent, R.P.: Algorithms for Minimisation Without Derivatives. Prentice-Hall, Englewood Cliffs (1973)zbMATHGoogle Scholar
  2. 2.
    Canny, J.: A computational approach to edge detection. TPAMI 8(6), 679–698 (1986)CrossRefGoogle Scholar
  3. 3.
    Devernay, F.: A non-maxima suppression method for edge detection with sub-pixel accuracy. Technical Report 2724, INRIA Sophia Antipolis (1995)Google Scholar
  4. 4.
    Edelsbrunner, H., Mücke, E.P.: Three-dimensional alpha shapes. ACM Trans. Graph. 13(1), 43–72 (1994)CrossRefzbMATHGoogle Scholar
  5. 5.
    Jonker, P.P.: Skeletons in n dimensions using shape primitives. Pattern Recognition Letters 23, 677–686 (2002)CrossRefzbMATHGoogle Scholar
  6. 6.
    Köthe, U.: Vigra. Web Resource, http://hci.iwr.uni-heidelberg.de/vigra/ (visited March 1, 2009)
  7. 7.
    Köthe, U.: Reliable Low-Level Image Analysis. Habilitation thesis, University of Hamburg, Germany (2008)Google Scholar
  8. 8.
    Luo, L., Hamitouche, C., Dillenseger, J., Coatrieux, J.: A moment-based three-dimensional edge operator. IEEE Trans. Biomed. 40(7), 693–703 (1993)CrossRefGoogle Scholar
  9. 9.
    Mendonça, P.R.S., Padfield, D.R., Miller, J., Turek, M.: Bias in the localization of curved edges. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3022, pp. 554–565. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Monga, O., Deriche, R., Rocchisani, J.: 3d edge detection using recursive filtering: application to scanner images. CVGIP: Image Underst. 53(1), 76–87 (1991)CrossRefzbMATHGoogle Scholar
  11. 11.
    Moré, J.J., Thuente, D.J.: Line search algorithms with guaranteed sufficient decrease. ACM Trans. Math. Software 20, 286–307 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Udupa, J.K., Hung, H.M., Chuang, K.S.: Surface and volume rendering in three dimensional imaging: A comparison. J. Digital Imaging 4, 159–169 (1991)CrossRefGoogle Scholar
  13. 13.
    Unser, M., Aldroubi, A., Eden, M.: B-Spline signal processing: Part I—Theory. IEEE Trans. Signal Process. 41(2), 821–833 (1993)CrossRefzbMATHGoogle Scholar
  14. 14.
    Unser, M., Aldroubi, A., Eden, M.: B-Spline signal processing: Part II—Efficient design and applications. IEEE Trans. Signal Process. 41(2), 834–848 (1993)CrossRefzbMATHGoogle Scholar
  15. 15.
    Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C++: The Art of Scientific Computing. Cambridge University Press, Cambridge (2002)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christian Bähnisch
    • 1
    • 2
  • Peer Stelldinger
    • 1
    • 2
  • Ullrich Köthe
    • 1
    • 2
  1. 1.University of HamburgHamburgGermany
  2. 2.University of HeidelbergHeidelbergGermany

Personalised recommendations