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Dynamic Medial Axes of Planar Shapes

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Advances in Computer Graphics (CGI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4035))

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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.

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References

  1. Alt, H., Cheong, O., Vigneron, A.: The Voronoi diagram of curved objects. Discrete & Computational Geometry 34(3), 439–453 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blum, H.: Biological shape and visual science. Journal of Theoretical Biology 38, 205–287 (1973)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  5. Farouki, R.T., Ramamurthy, R.: Specified-precision computation of curve/curve bisectors. Internat. J. Comput. Geom. Appl. 8(5-6), 599–617 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kimmel, R., Shaked, D., Kiryati, N.: Skeletonization via diatance maps and level sets. Computer Vision and Image Understanding 62(3), 382–391 (1995)

    Article  Google Scholar 

  7. Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagram, 2nd edn. John Wiley, Chichester (2000)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. The Hong Kong University of Science and Technology,  

    Kai Tang

  2. Tsinghua University, Beijing, P.R. China

    Yongjin Liu

Authors
  1. Kai Tang
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  2. Yongjin Liu
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Editor information

Editors and Affiliations

  1. The University of Tokyo,, P.O. Box

    Tomoyuki Nishita

  2. State Key Lab. of CAD&CG, Zhejiang Univerisity,, 310027, Hangzhou, China

    Qunsheng Peng

  3. Max Planck Institute for Computer Science, Saarbrücken, Germany

    Hans-Peter Seidel

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© 2006 Springer-Verlag Berlin Heidelberg

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Tang, K., Liu, Y. (2006). Dynamic Medial Axes of Planar Shapes. In: Nishita, T., Peng, Q., Seidel, HP. (eds) Advances in Computer Graphics. CGI 2006. Lecture Notes in Computer Science, vol 4035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11784203_40

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