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Unification of Nonlinear Filtering in the Context of Binary Logical Calculus, Part I: Binary Filters

  • Edward R. Dougherty
  • Robert M. Haralick

Abstract

The mathematical structure of nonlinear filtering is expressed in the context of binary logic. This first part of a two-part study concerns the binary setting. Operator properties, such as antiextensivity and idempotence, are expressed in finite logical expressions, as are the Matheron representation for morphological filters and its extension to translation-invariant operators, thereby giving simplicity to both operational properties and representations and also exposing the manner in which logic methods can be used for filter design and analysis. The second part of the study treats gray-scale filters.

Key words

nonlinear filter morphological filter image algebra representation cellular logic 

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Edward R. Dougherty
    • 1
  • Robert M. Haralick
    • 2
  1. 1.Center for Imaging ScienceRochester Institute of TechnologyRochesterUSA
  2. 2.Department of Electrical EngineeringUniversity of WashingtonSeattleUSA

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