Dual complexes of cubical subdivisions of ℝn

H. Edelsbrunner, M. Kerber, Discrete & Computational Geometry 47 (2012) 393–414.

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Journal Article | Published | English
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Abstract
We use a distortion to define the dual complex of a cubical subdivision of ℝ n as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ n.
Publishing Year
Date Published
2012-03-01
Journal Title
Discrete & Computational Geometry
Acknowledgement
This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0057 and HR0011-09-0065 as well as the National Science Foundation (NSF) under grant DBI-0820624.
Volume
47
Issue
2
Page
393 - 414
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Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 2012;47(2):393-414. doi:10.1007/s00454-011-9382-4
Edelsbrunner, H., & Kerber, M. (2012). Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry, 47(2), 393–414. https://doi.org/10.1007/s00454-011-9382-4
Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry 47, no. 2 (2012): 393–414. https://doi.org/10.1007/s00454-011-9382-4.
H. Edelsbrunner and M. Kerber, “Dual complexes of cubical subdivisions of ℝn,” Discrete & Computational Geometry, vol. 47, no. 2, pp. 393–414, 2012.
Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 47(2), 393–414.
Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry, vol. 47, no. 2, Springer, 2012, pp. 393–414, doi:10.1007/s00454-011-9382-4.
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