Minkowski Functionals Study of Random Number Sequences

  • Authors:

  • Xinyu Zhang;Seth Watts;Yaohang Li;Daniel Tortorelli

  • Affiliations:

  • College of Engineering, North Carolina A&T State University, Greensboro NC 27411;Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801;Department of Computer Science, North Carolina A&T State University, Greensboro, NC 27411;Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

  • Venue:
  • ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
  • Year:
  • 2009

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Abstract

Random number sequences are used in a wide range of applications such as simulation, sampling, numerical analysis, cryptography, and recreation. The quality of random number sequences is critical to the correctness of these applications. Many statistical tests have been developed to test various characteristics of random number generators such as randomness, independence, uniformity, etc. Most of them are based on testing on a single sequence. When multiple sequences are employed in an application, their potential correlations are also concerned. In this paper, we explore the techniques of using the Minkowski functionals and their extensions, the Minkowski valuations, to study the mathematical morphology of two dimensional binary image generated by pair-wise random number sequences, and apply this method to describe and compare the properties of several well-known pseudo- and quasi-random number generators.