Discrete & Computational Geometry

, Volume 56, Issue 1, pp 93–113

Intrinsic Volumes of Random Cubical Complexes

Article

DOI: 10.1007/s00454-016-9789-z

Cite this article as:
Werman, M. & Wright, M.L. Discrete Comput Geom (2016) 56: 93. doi:10.1007/s00454-016-9789-z

Abstract

Intrinsic volumes, which generalize both Euler characteristic and Lebesgue volume, are important properties of d-dimensional sets. A random cubical complex is a union of unit cubes, each with vertices on a regular cubic lattice, constructed according to some probability model. We analyze and give exact polynomial formulae, dependent on a probability, for the expected value and variance of the intrinsic volumes of several models of random cubical complexes. We then prove a central limit theorem for these intrinsic volumes. For our primary model, we also prove an interleaving theorem for the zeros of the expected-value polynomials. The intrinsic volumes of cubical complexes are useful for understanding the shape of random d-dimensional sets and for characterizing noise in applications.

Keywords

Intrinsic volume Cubical complex Random complex Euler characteristic 

Mathematics Subject Classification

60D05 52C99 

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.The Hebrew University of JerusalemJerusalemIsrael
  2. 2.St. Olaf CollegeNorthfieldUSA

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