Intrinsic Volumes of Random Cubical Complexes

Michael Werman, Matthew L. Wright

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)93-113
Number of pages21
JournalDiscrete and Computational Geometry
Volume56
Issue number1
DOIs
StatePublished - 1 Jul 2016

Keywords

  • Cubical complex
  • Euler characteristic
  • Intrinsic volume
  • Random complex

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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