Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice

Volume 265 of the series Studies in Fuzziness and Soft Computing pp 229-253

Two Methods for Image Compression/Reconstruction Using OWA Operators

  • H. BustinceAffiliated withUniversidad Pública de Navarra
  • , D. PaternainAffiliated withUniversidad Pública de Navarra
  • , B. De BaetsAffiliated withDept. of Applied Mathematics, Biometrics and Process Control, Universiteit Gent
  • , T. CalvoAffiliated withUniversidad de Alcalá
  • , J. FodorAffiliated withInstitute of Intelligent Engineering Systems, Budapest Tech
  • , R. MesiarAffiliated withDepartment of Mathematics and Descriptive Geometry, Slovak University of Technology
  • , J. MonteroAffiliated withFacultad de Matemáticas, Universidad Complutense
  • , A. PraderaAffiliated withDepartamento de Ciencias de la Computación, Universidad Rey Juan Carlos

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In this chapter we address image compression by means of two alternative algorithms. In the first algorithm, we associate to each image an interval-valued fuzzy relation, and we build an image which is n times smaller than the original one, by using two-dimensional OWA operators. The experimental results show that, in this case, best results are obtained with ME-OWA operators. In the second part of the work, we describe a reduction algorithm that replaces the image by several eigen fuzzy sets associated with it. We obtain these eigen fuzzy sets by means of an equation that relates the OWA operators we use and the relation (image) we consider. Finally, we present a reconstruction method based on an algorithm which minimizes a cost function, with this cost function built by means of two-dimensional OWA operators.