Any open bounded subset of Rn has the same homotopy type than its medial axis

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Any open bounded subset of Rⁿ has the same homotopy type than its medial axis

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ACM Symposium on Solid and Physical Modeling archive
Proceedings of the eighth ACM symposium on Solid modeling and applications table of contents

Seattle, Washington, USA

SESSION: Skeletal/medial axis representations table of contents

Pages: 65 - 75

Year of Publication: 2003

ISBN:1-58113-706-0

Author

André Lieutier

Dassault Systemes (Aix-en-provence) and LMC-IMAG (Grenoble), France

Sponsors

ACM: Association for Computing Machinery
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 7, Downloads (12 Months): 43, Citation Count: 10

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ABSTRACT

Medial Axis Transform is sometimes used as an intermediate representation in algorithms for meshing or recognition of shapes from digitized data. This raises the question whether the Medial Axis captures fundamental topological invariants of the object. The (positive) answer has been known already in the case of smooth objects. The main result presented here is the homotopy equivalence of any bounded open subset of Rⁿ with its Medial Axis.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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CITED BY 10

	Jehoshua Bruck , Jie Gao , Anxiao (Andrew) Jiang, MAP: medial axis based geometric routing in sensor networks, Proceedings of the 11th annual international conference on Mobile computing and networking, August 28-September 02, 2005, Cologne, Germany
	Avneesh Sud , Mark Foskey , Dinesh Manocha, Homotopy-preserving medial axis simplification, Proceedings of the 2005 ACM symposium on Solid and physical modeling, p.39-50, June 13-15, 2005, Cambridge, Massachusetts
	Frédéric Chazal , David Cohen-Steiner, A condition for isotopic approximation, Proceedings of the ninth ACM symposium on Solid modeling and applications, June 09-11, 2004, Genoa, Italy
	F. Chazal , A. Lieutier, Stability and homotopy of a subset of the medial axis, Proceedings of the ninth ACM symposium on Solid modeling and applications, June 09-11, 2004, Genoa, Italy
	Jehoshua Bruck , Jie Gao , Anxiao Jiang, Map: medial axis based geometric routing in sensor networks, Wireless Networks, v.13 n.6, p.835-853, December 2007
	Balint Miklos , Joachim Giesen , Mark Pauly, Medial axis approximation from inner Voronoi balls: a demo of the Mesecina tool, Proceedings of the twenty-third annual symposium on Computational geometry, June 06-08, 2007, Gyeongju, South Korea
	Frederic Cazals , Aditya Parameswaran , Sylvain Pion, Robust construction of the three-dimensional flow complex, Proceedings of the twenty-fourth annual symposium on Computational geometry, June 09-11, 2008, College Park, MD, USA
	Eitan Yaffe , Dan Halperin, Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space, Proceedings of the twenty-fourth annual symposium on Computational geometry, June 09-11, 2008, College Park, MD, USA
	Nicu D. Cornea , Deborah Silver , Patrick Min, Curve-Skeleton Properties, Applications, and Algorithms, IEEE Transactions on Visualization and Computer Graphics, v.13 n.3, p.530-548, May 2007
	Xianjin Zhu , Rik Sarkar , Jie Gao, Segmenting a sensor field: Algorithms and applications in network design, ACM Transactions on Sensor Networks (TOSN), v.5 n.2, p.1-32, March 2009