Decomposition and Construction of Neighbourhood Operations Using Linear Algebra

  • Atsushi Imiya
  • Yusuke Kameda
  • Naoya Ohnishi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)


In this paper, we introduce a method to express a local linear operated in the neighbourhood of each point in the discrete space as a matrix transform. To derive matrix expressions, we develop a decomposition and construction method of the neighbourhood operations using algebraic properties of the noncommutative matrix ring. This expression of the transforms in image analysis clarifies analytical properties, such as the norm of the transforms. We show that the symmetry kernels for the neighbourhood operations have the symmetry matrix expressions.


Construction Method Digital Image Processing Kronecker Product Digital Image Analysis Algebraic Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Atsushi Imiya
    • 1
    • 2
  • Yusuke Kameda
    • 1
    • 2
  • Naoya Ohnishi
    • 1
    • 2
  1. 1.Institute of Media and Information TechnologyChiba UniversityJapan
  2. 2.School of Science and TechnologyChiba UniversityJapan

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