Spherical CIELab QAMs: Associative Memories Based on the CIELab System and Quantales for the Storage of Color Images

摘要

A quantale is the mathematical structure obtained by enriching a complete lattice with an associative binary operation which commutes with the supremum operation. We refer to an associative memory model that performs operations in a quantale as a quantale-based associative memory (QAM). Examples of QAMs include many lattice-based models such as gray-scale morphological associative memories and implicative fuzzy associative memories. Besides introducing auto-associative QAMs, this paper presents a QAM model for the storage and recall of color patterns. Specifically, novel QAM models, referred to as spherical CIELab QAMs, are defined in terms of the spherical coordinates of the CIELab system with an ordering scheme and a binary operation that yields a quantale. Computational experiments reveal that the spherical CIELab QAMs exhibit some tolerance with respect to impulsive noise.