THE ORDER OF A 2-SEQUENCE AND THE COMPLEXITY OF DIGITAL IMAGES

Tadas Telksnys (), Zenonas Navickas (), Martynas Vaidelys () and Minvydas Ragulskis ()
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Tadas Telksnys: Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania
Zenonas Navickas: Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania
Martynas Vaidelys: Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania
Minvydas Ragulskis: Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

Advances in Complex Systems (ACS), 2016, vol. 19, issue 04n05, 1-25

Abstract: The concept of the order of a 2-sequence is introduced in this paper. The order of a 2-sequence is a natural but not trivial extension of the order of one-dimensional (1D) linear recurrent sequences. Necessary and sufficient conditions for the generation of 2-sequences with finite order from the minimal information subset are derived. It is demonstrated that the order of 2-sequences can be used to estimate the complexity of self-organizing patterns with respect to each spatial coordinate.

Keywords: Linear recurrent sequence; Hankel matrix; algebraic decomposition; image complexity (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0219525916500107

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