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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alt, H., Cheong, O., Vigneron, A.: The Voronoi diagram of curved objects. Discrete & Computational Geometry 34(3), 439–453 (2005)
Blum, H.: Biological shape and visual science. Journal of Theoretical Biology 38, 205–287 (1973)
Choi, H.I., Choi, S.W., Moon, H.P.: Mathematical theory of medial axis transform. Pacific Journal of Mathematics 181(1), 57–88 (1997)
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)
Farouki, R.T., Ramamurthy, R.: Specified-precision computation of curve/curve bisectors. Internat. J. Comput. Geom. Appl. 8(5-6), 599–617 (1998)
Kimmel, R., Shaked, D., Kiryati, N.: Skeletonization via diatance maps and level sets. Computer Vision and Image Understanding 62(3), 382–391 (1995)
Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagram, 2nd edn. John Wiley, Chichester (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/11784203_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35638-7
Online ISBN: 978-3-540-35639-4
eBook Packages: Computer ScienceComputer Science (R0)