Extended Associative Memories for Recalling Gray Level Patterns

  • Humberto Sossa
  • Ricardo Barrón
  • Francisco Cuevas
  • Carlos Aguilar
  • Héctor Cortés
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3287)

Abstract

We show how the binary αβ associative memories recently proposed by Yáñez in [1] can be extended to work now in the gray-level case. To get the desired extension we take the operators α and β, foundation of the αβ memories, and propose a more general family of operators among them the original operators α and β are a subset. For this we formulate a set of functional equations, solve this system and find a family of solutions. We show that the α and β originally proposed in [1] are just a particular case of this new family. We give the properties of the new operators. We then use these operators to build the extended memories. We provide the conditions under which the proposed extended memories are able to recall a pattern either from the pattern’s fundamental set or from altered versions of them. We provide real examples with images where the proposed memories show their efficiency.

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References

  1. 1.
    Yáñez, C.: Associative Memories based on Order Relations and Binary Operators (In Spanish), PhD Thesis, Center for Computing Research (February 2002)Google Scholar
  2. 2.
    Dhombres, A.: Functional Equations Containing Several Variables. Cambridge University Press, Cambridge (1991)Google Scholar
  3. 3.
    Aczel, J.: Functional Equations: History, Applications and Theory. Kluwer Academic Pub. Group, Dordrecht (1984)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Humberto Sossa
    • 1
  • Ricardo Barrón
    • 1
  • Francisco Cuevas
    • 2
  • Carlos Aguilar
    • 1
  • Héctor Cortés
    • 1
  1. 1.Centro de Investigación en Computación IPNEsquina con Miguel Othón de Mendizábal, Colonia Nueva Industrial VallejoMéxico, D. F.Mexico
  2. 2.Centro de Investigaciones en Óptica, A. C.LeónMéxico

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