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Medial axis approximation from inner Voronoi balls: a demo of the Mesecina tool

Published:06 June 2007Publication History

ABSTRACT

We illustrate a simple algorithm for approximating the medial axis of a 2D shape with smooth boundary from a sample of this boundary. The algorithm is compared to a more general approximation method that builds on the same idea, namely, to approximate the shape by a union of balls. While not as general, our algorithm is simpler, faster and numerically more stable. Both algorithms are visualized using the Mesecina tool, which is also described.

References

  1. Computational Geometry Algorithms Library. http://www.cgal.org/.Google ScholarGoogle Scholar
  2. CORE library. http://cs.nyu.edu/exact/core/.Google ScholarGoogle Scholar
  3. Nina Amenta, Marshall Bern, and David Eppstein. The crust and the beta--skeleton: combinatorial curve reconstruction. Graph. Models Image Process., 60(2):125--35, 1998. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Nina Amenta, Sunghee Choi, and Ravi Kolluri. The power crust, unions of balls, and the medial axis transform. Computational Geometry: Theory and Applications, 19(2--3):127--153, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Nina Amenta and Ravi Krishna Kolluri. The medial axis of a union of balls. Comput. Geom. Theory Appl., 20(1--2):25--37, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Dominique Attali and Annick Montanvert. Computing and simplifying 2D and 3D continuous skeletons. Comput. Vis. Image Underst., 67(3):261--273, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. André Lieutier. Any open bounded subset of Rn has the same homotopy type than its medial axis. In SM'03: Proceedings of the eighth ACM symposium on Solid modeling and applications, pages 65--75, New York, NY, USA, 2003. ACM Press. Google ScholarGoogle ScholarDigital LibraryDigital Library

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  1. Medial axis approximation from inner Voronoi balls: a demo of the Mesecina tool

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        • Published in

          cover image ACM Conferences
          SCG '07: Proceedings of the twenty-third annual symposium on Computational geometry
          June 2007
          404 pages
          ISBN:9781595937056
          DOI:10.1145/1247069
          • Program Chair:
          • Jeff Erickson

          Copyright © 2007 ACM

          Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 6 June 2007

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          Overall Acceptance Rate625of1,685submissions,37%

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