Non-centered Voronoi Skeletons

  • Maximilian LangerEmail author
  • Aysylu Gabdulkhakova
  • Walter G. Kropatsch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)


We propose a novel Voronoi Diagram based skeletonization algorithm that produces non-centered skeletons. The first strategy considers utilizing Elliptical Line Voronoi Diagrams with varied density based sampling of the polygonal shapes. The second strategy applies a weighting scheme on Elliptical Line Voronoi Diagrams and Line Voronoi Diagrams. The proposed skeletonization algorithm uses precomputed distance fields and basic element-wise operations, thus can be easily adapted for parallel execution. Non-centered Voronoi Skeletons give a representation that is more similar to real world skeletons and retain many of the desirable properties of skeletons.


Generalized Voronoi Diagram Line Voronoi Voronoi Skeleton Elliptical distance Weighted hausdorff 


  1. 1.
    Blum, H.: A transformation for extracting descriptors of shape. In: Models for the Perception of Speech and Visual Form (1967)Google Scholar
  2. 2.
    Boada, I., Coll, N., Madern, N., Antoni Sellares, J.: Approximations of 2D and 3D generalized voronoi diagrams. Int. J. Comput. Math. 85(7), 1003–1022 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gabdulkhakova, A., Kropatsch, W.G.: Confocal ellipse-based distance and confocal elliptical field for polygonal shapes. In: Proceedings of the 24th International Conference on Pattern Recognition, ICPR (2018)Google Scholar
  4. 4.
    Gabdulkhakova, A., Langer, M., Langer, B.W., Kropatsch, W.G.: Line Voronoi diagrams using elliptical distances. In: Bai, X., Hancock, E.R., Ho, T.K., Wilson, R.C., Biggio, B., Robles-Kelly, A. (eds.) S+SSPR 2018. LNCS, vol. 11004, pp. 258–267. Springer, Cham (2018). Scholar
  5. 5.
    Held, M.: Voronoi diagrams and offset curves of curvilinear polygons. Comput.-Aided Des. 30(4), 287–300 (1998)CrossRefGoogle Scholar
  6. 6.
    Kalra, N., Ferguson, D., Stentz, A.: Incremental reconstruction of generalized voronoi diagrams on grids. Robot. Auton. Syst. 57(2), 123–128 (2009)CrossRefGoogle Scholar
  7. 7.
    Klein, R., Langetepe, E., Nilforoushan, Z.: Abstract Voronoi diagrams revisited. Comput. Geom. 42(9), 885–902 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lee, D.T.: Medial axis transformation of a planar shape. IEEE Trans. Pattern Anal. Mach. Intell. 4(4), 363–369 (1982)CrossRefGoogle Scholar
  9. 9.
    Mayya, N., Rajan, V.: Voronoi diagrams of polygons: a framework for shape representation. J. Math. Imaging Vis. 6(4), 355–378 (1996)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Ogniewicz, R., Ilg, M.: Voronoi skeletons: theory and applications. In: Proceedings of 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 1992 (1992)Google Scholar
  11. 11.
    Ogniewicz, R.L.: Discrete Voronoi skeletons. Ph.D. thesis, ETH Zurich (1992)Google Scholar
  12. 12.
    Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. Wiley, Hoboken (2009)zbMATHGoogle Scholar
  13. 13.
    Saha, P., Borgefors, G., Sanniti di Baja, G.: Skeletonization: Theory, Methods, and Applications (2017)CrossRefGoogle Scholar
  14. 14.
    Setter, O., Sharir, M., Halperin, D.: Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space. In: Gavrilova, M.L., Tan, C.J.K., Anton, F. (eds.) Transactions on Computational Science IX. LNCS, vol. 6290, pp. 1–27. Springer, Heidelberg (2010). Scholar
  15. 15.
    Strzodka, R., Telea, A.: Generalized distance transforms and skeletons in graphics hardware. In: Proceedings of the Sixth Joint Eurographics-IEEE TCVG Conference on Visualization. Eurographics Association (2004)Google Scholar
  16. 16.
    Vleugels, J.M., Overmars, M.H.: Approximating generalized Voronoi diagrams in any dimension. Utrecht University (1995)Google Scholar
  17. 17.
    Yuan, Z., Rong, G., Guo, X., Wang, W.: Generalized Voronoi diagram computation on GPU. In: 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD) (2011)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maximilian Langer
    • 1
    Email author
  • Aysylu Gabdulkhakova
    • 1
  • Walter G. Kropatsch
    • 1
  1. 1.Pattern Recognition and Image Processing Group, 193-03 Institute of Visual Computing and Human-Centered TechnologyTechnische Universität WienViennaAustria

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