Abstract
Medial Axis Transform (MAT) is a representation that encodes an object with symmetric (medial) axes in the object interior. MAT has been employed in a variety of applications such as pattern recognition of digital images, biological shape analysis and robotic motion planning. Although numerous algorithms have been proposed to determine MAT of polygonal objects, a robust model for arbitrarily shaped regions, especially suitable for engineering designs, is still an active area of research. In this paper, a 2D approach capable of efficiently constructing MAT for arbitrarily shaped 2D regions is proposed. This method can be utilized to evaluate 3D objects for a variety of applications though it does not produce a 3D MAT. Alternatively, an algorithm for calculating the MAT of 3D polyhedra is also presented.
Chapter PDF
Similar content being viewed by others
References
U. Montanari. Continuous skeletons from digitized images. Journal of the Association for Computing Machinery, 16 (4): 534–549, October 1969.
H. N. Gursoy. Shape Interrogation by Medial Axis Transform for Automated Analysis. Ph.D. thesis, Massachusetts Institute of Technology, 1989.
N. M. Patrikalakis and H. N. Gursoy. Shape interrogation by medial axis transform. Advances in Design Automation, 23: 77–88, 1990.
S. N. Meshkat and C. M. Sakkas. Voronoi diagram for multiply-connected polygonal domains ii: Implementation and application. IBM Journal of Research and Development, 31 (3): 373–381, May 1987.
H. Persson. Nc machining of arbitrarily shaped pockets. Computer-Aided Design, 10(3):169174, May 1978.
M. Held. On the Computational Geometry of Pocket Machining. Springer Verlag, Berlin Heidelberg, 1991.
M. Rezayat. Midsurface abstraction from 3d solid models: General theory and applications. Computer-Aided Design, 28 (11): 905–915, 1996.
M. Shapiro and A. Rappoport. Shape blending using the star-skeleton representation. IEEE Computer Graphics and Applications, 15 (2): 44–50, March 1995.
R. Radhakrishnan, A. Amsalu, M. Kamran, and B. O. Nnaji. Design rule checker for sheet metal components using medial axis transformation and geometric reasoning. Journal of Manufacturing Systems, 15 (3): 179–189, 1996.
B. T. Cheok, Y. F. Zhang, and L. F. Leow. A skeleton-retrieving approach for the recognition of punch shapes. Computers in Industry, 32 (3): 249–259, March 1997.
J.-C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Norwell, Massachusetts, 1991.
R. Gadh, L. E. G“ ursoz, M. A. Hall, and F. B. Prinz. Feature abstraction in a knowledge-based critique of designs. Manufacturing Review, 4 (2): 115–125, June 1991.
H. Blum. A transformation for extracting new descriptors of shape. In W. Wathen-Dunn, editor, Models for the Perception of Speech and Visual Form, 326–380, Cambridge, MA, 1967. The M.I.T. Press.
J.-H. Kao. Process planning for additive/subtractive solid freeform fabrication using medial axis transform. Ph.D. thesis, Department of Mechanical Engineering, Stanford University, Stanford, California, 1997.
R. Joan-Arinyo, L. Perez-Vidal, and E. Gargallo-Monllau. An adaptive algorithm to compute the medial axis transform of 2D polygonal domains. In D. Roller and P. Brunet, editors, CAD Systems Development, 283–298, Springer Verlag, 1997.
T. Culver. Computing the medial axis of a polyhedron reliably and efficiently. Ph.D. thesis, Department of Computer Science, University of North Carolina at Chapel Hill, 2000.
R. Joan-Arinyo, L. Perez-Vidal, and J. Vilaplana. Computing the Medial Axis Transform of Polygonal Domains by Tracing Paths. Llenguatges i Sistemes Informàtics Report LSI-99–8-R, Universitat Politecnica de Catalunya, April 1999.
E. C. Sherbrooke, N. M. Patrikalakis, and E. Brisson. An algorithm for the medial axis transform of 3d polyhedral solids. IEEE Transactions on Visualization and Computer Graphics, 2 (1): 44–61, Match 1996.
H. I. Choi, S. W. Choi, and H. P. Moon. New algorithm for medial axis transform of plane domain. Graphical Models and Image Processing, 59 (6): 463–483, November 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Chang, YC., Kao, JH., Pinilla, J.M., Dong, J., Prinz, F.B. (2001). Medial Axis Transform (MAT) of General 2D Shapes and 3D Polyhedra for Engineering Applications. In: Kimura, F. (eds) Geometric Modelling. GEO 1998. IFIP — The International Federation for Information Processing, vol 75. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35490-3_3
Download citation
DOI: https://doi.org/10.1007/978-0-387-35490-3_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-5322-6
Online ISBN: 978-0-387-35490-3
eBook Packages: Springer Book Archive