Advertisement

Dynamic Medial Axes of Planar Shapes

  • Kai Tang
  • Yongjin Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4035)

Abstract

In this paper a computational model called dynamic medial axis (\(\mathcal{DMA}\)) is proposed to describe the internal evolution of planar shapes. To define the \(\mathcal{DMA}\), a symbolic representation called matching list is proposed to depict the topological structure of the medial axis. As shown in this paper with provable properties, the \(\mathcal{DMA}\) exhibits an interesting dynamic skeleton structure for planar shapes. Finally an important application of the proposed \(\mathcal{DMA}\) — computing the medial axis of multiply-connected planar shapes with curved boundaries — is presented.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alt, H., Cheong, O., Vigneron, A.: The Voronoi diagram of curved objects. Discrete & Computational Geometry 34(3), 439–453 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Blum, H.: Biological shape and visual science. Journal of Theoretical Biology 38, 205–287 (1973)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Choi, H.I., Choi, S.W., Moon, H.P.: Mathematical theory of medial axis transform. Pacific Journal of Mathematics 181(1), 57–88 (1997)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Farouki, R.T., Johnstone, J.K.: The bisector of a point and a plane parametric curve. Computer Aided Geometric Design 11(2), 117–151 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Farouki, R.T., Ramamurthy, R.: Specified-precision computation of curve/curve bisectors. Internat. J. Comput. Geom. Appl. 8(5-6), 599–617 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Kimmel, R., Shaked, D., Kiryati, N.: Skeletonization via diatance maps and level sets. Computer Vision and Image Understanding 62(3), 382–391 (1995)CrossRefGoogle Scholar
  7. 7.
    Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagram, 2nd edn. John Wiley, Chichester (2000)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kai Tang
    • 1
  • Yongjin Liu
    • 2
  1. 1.The Hong Kong University of Science and Technology 
  2. 2.Tsinghua UniversityBeijingP.R. China

Personalised recommendations