Dual complexes of cubical subdivisions of ℝn Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Kerber, Michael ; https://orcid.org/0000-0002-8030-9299 ddc:000 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. Springer 2012 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/3256 https://research-explorer.ista.ac.at/download/3256/4675 Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. <i>Discrete &#38; Computational Geometry</i>. 2012;47(2):393-414. doi:<a href="https://doi.org/10.1007/s00454-011-9382-4">10.1007/s00454-011-9382-4</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00454-011-9382-4 info:eu-repo/semantics/altIdentifier/wos/000299057200010 info:eu-repo/semantics/openAccess