The scale axis transform

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2009, Pages 106-115

  Giesen, Joachim ^a   Miklos, Balint ^b   Pauly, Mark ^b   Wormser, Camille ^b  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b ETH ZURICH   (Switzerland)

Author keywords

Medial axis; Skeleton; Topology

Indexed keywords

DISCRETE APPROXIMATION; DISTANCE FUNCTIONS; MEDIAL AXIS; MEDIAL AXIS TRANSFORMS; SHAPE REPRESENTATION; STEEPEST ASCENT; THEORETICAL RESULT; TOPOLOGICAL PROPERTIES;

MATHEMATICAL TRANSFORMATIONS; TOPOLOGY;

COMPUTATIONAL GEOMETRY;

EID: 70849105935     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1542362.1542388     Document Type: Conference Paper

References (18)

1. Cgal, Computational Geometry Algorithms Library. http://www.cgal.org.
2. Nina Amenta, Sunghee Choi, and Ravi Krishna Kolluri. The power crust. In SMA '01: Proceedings of the sixth ACM symposium on Solid modeling and applications, pages 249-266, New York, NY, USA, 2001. ACM.
3. Dominique Attali, Jean-Daniel Boissonnat, and Herbert Edelsbrunner. Stability and computation of the medial axis - a state-of-the-art report. Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, 2007.
4. Jean-Daniel Boissonnat, Camille Wormser, and Mariette Yvinec. Curved Voronoi diagrams. In Jean-Daniel Boissonnat and Monique Teillaud, editors, Effective Computational Geometry for Curves and Surfaces, pages 67-116. Springer-Verlag, Mathematics and Visualization, 2006.
5. Kevin Buchin, Tamal K. Dey, Joachim Giesen, and Matthias John. Recursive geometry of the flow complex and topology of the flow complex filtration. Comput. Geom. Theory Appl., 40(2):115-137, 2008.
6. Piermarco Cannarsa and Carlo Sinestrari. Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control. Birkhäuser, Boston, USA, 2004.
7. Frédéric Chazal and André Lieutier. The λ-medial axis. Graphical Models, 67(4):304-331, 2005.
8. Marc-Olivier Czarnecki and Ludovic Rifford. Approximation and regularization of Lipschitz functions: Convergence of the gradients. Transactions-American Mathematical Society, 358(10):4467, 2006.
9. Tamal Dey and Wulue Zhao. Approximate medial axis as a Voronoi subcomplex. Computer-Aided Design, 36(2):195-202, 2004.
10. Herbert Edelsbrunner. Deformable smooth surface design. Discrete & Computational Geometry, 21(1):87-115, 1999.
11. Karsten Grove and Katsuhiro Shiohama. A generalized sphere theorem. The Annals of Mathematics, 106(1):201-211, 1977.
12. André Lieutier. Any open bounded subset of R n has the same homotopy type as its medial axis. Computer-Aided Design, 36(11):1029-1046, 2004.
13. Anton Petrunin. Semiconcave functions in Alexandrov's geometry. In Surveys in Differential Geometry: Metric and Comparison Geometry, volume XI. Internationational Press of Boston, 2007.
14. Stephen M. Pizer, Kaleem Siddiqi, Gabor Székely, James N. Damon, and Steven W. Zucker. Multiscale medial loci and their properties. Int. J. Comput. Vision, 55(2-3):155-179, 2003.
15. R. Tyrrell Rockafellar and Roger J.-B. Wets. Variational Analysis. Springer, 1997.
16. Avneesh Sud, Mark Foskey, and Dinesh Manocha. Homotopy-preserving medial axis simplification. Proceedings of the 2005 ACM symposium on Solid and physical modeling, pages 39-50, 2005.
17. Roger C. Tam and Wolfgang Heidrich. Feature-preserving medial axis noise removal. In ECCV '02: Proceedings of the 7th European Conference on Computer Vision-Part II, pages 672-686, London, UK, 2002. Springer-Verlag.
18. Xiaofei Wang and Christina A. Burbeck. Scaled medial axis representation: evidence from position discrimination task. Vision Research, 38(13):1947-1958, 1998.