Polygon Mesh Generation of Branching Structures

  • Jo Skjermo
  • Ole Christian Eidheim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3540)


We present a new method for producing locally non intersecting polygon meshes of naturally branching structures. The generated polygon mesh follows the object’s underlying structure as close as possible, while still producing polygon meshes that can be visualized efficiently on commonly available graphic acceleration hardware. A priori knowledge of vascular branching systems is used to derive the polygon mesh generation method. Visualization of the internal liver vessel structures and naturally looking tree stems generated by Lindenmayer-systems is used as examples. The method produce visually convincing polygon meshes that might be used in clinical applications in the future.


Augmented Reality Hepatic Vessel Mesh Production Middle Cross Section Parent Segment 
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.


  1. 1.
    Bloomenthal, J.: Modeling the mighty maple. Computer Graphics 19(3), 305–311 (1985)CrossRefGoogle Scholar
  2. 2.
    Bloomenthal, J., Wyvill, B.: Interactive techniques for implicit modeling. Computer Graphics 24(2), 109–116 (1990)CrossRefGoogle Scholar
  3. 3.
    Catmull, E., Clark, J.: Recursively generated b-spline surfaces on arbitrary topological meshes. Computer Aided Design 10(6), 350–355 (1978)CrossRefGoogle Scholar
  4. 4.
    Chaudhuri, S., Chatterjee, S., Katz, N., Nelson, M., Goldbaum, M.: Detection of blood vessels in retinal images using two-dimensional matched filters. IEEE Transactions on Medical Imageing 8(3), 263–269 (1989)CrossRefGoogle Scholar
  5. 5.
    Eidheim, O.C., Aurdal, L., Omholt-Jensen, T., Mala, T., Edwin, B.: Segmentation of liver vessels as seen in mr and ct images. Computer Assisted Radiology and Surgery, 201–206 (2004)Google Scholar
  6. 6.
    Felkel, P., Fuhrmann, A., Kanitsar, A., Wegenkittl, R.: Surface reconstruction of the branching vessels for augmented reality aided surgery. Analysis of Biomedical Signals and Images 16, 252–254 (2002); Proc. BIOSIGNAL 2002Google Scholar
  7. 7.
    Felkel, P., Kanitsar, A., Fuhrmann, A.L., Wegenkittl, R.: Surface Models of Tube Trees. Tech. Rep. TR VRVis 2002 008, VRVis (2002)Google Scholar
  8. 8.
    Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Prentice Hall, Englewood Cliffs (2002)Google Scholar
  9. 9.
    Hart, J., Baker, B.: Implicit modeling of tree surfaces. In: Proc. of Implicit Surfaces 1996, October1996, pp. 143–152 (1996)Google Scholar
  10. 10.
    Kapur, J.N., Sahoo, P.K., Wong, A.K.C.: A new method for gray-level picture thresholding using the entropy of the histogram. Computer Vision, Graphics, and Image Processing 29, 273–285 (1985)CrossRefGoogle Scholar
  11. 11.
    Lluch, J., Vicent, M., Fernandez, S., Monserrat, C., Vivo, R.: Modelling of branched structures using a single polygonal mesh. In: Proc. IASTED International Conference on Visualization, Imaging, and Image Processing (2001)Google Scholar
  12. 12.
    Maierhofer, S.: Rule-Based Mesh Growing and Generalized Subdivision Meshes. PhD thesis, Technische Universitaet Wien, Technisch-Naturwissenschaftliche Fakultaet, Institut fuer Computergraphik (2002)Google Scholar
  13. 13.
    Murray, C.D.: A relationship between circumference and weight in trees and its bearing in branching angles. Journal of General Phyiol. 9, 725–729 (1927)CrossRefGoogle Scholar
  14. 14.
    Oppenheimer, P.E.: Real time design and animation of fractal plants and trees. Computer Graphics 20(4), 55–64 (1986)CrossRefGoogle Scholar
  15. 15.
    Richter, J.P.: The notebooks of Leonardo da Vinc, vol. 1. Dover Pubns, Mineola (1970)Google Scholar
  16. 16.
    Soille, P.: Morphological Image Analysis. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  17. 17.
    Tobler, R.F., Maierhofer, S., Wilkie, A.: A multiresolution mesh generation approach for procedural definition of complex geometry. In: Proceedings of the 2002 International Conference on Shape Modelling and Applications (SMI 2002), pp. 35–43 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jo Skjermo
    • 1
  • Ole Christian Eidheim
    • 1
  1. 1.Department of Computer and Information ScienceNorwegian University of Science and Technology 

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