@article{3256,
  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.},
  author       = {Edelsbrunner, Herbert and Kerber, Michael},
  journal      = {Discrete & Computational Geometry},
  number       = {2},
  pages        = {393 -- 414},
  publisher    = {Springer},
  title        = {{Dual complexes of cubical subdivisions of ℝn}},
  doi          = {10.1007/s00454-011-9382-4},
  volume       = {47},
  year         = {2012},
}