Adaptive Median and Wiener Filters as Reference Functions for Morphological Associative Memories in Complete Inf-Semilattices

Mathematical morphology (MM) is a theory for nonlinear image and signal processing that was originally based on complete lattices and is usually still conducted in this framework. Later, MM was extended from complete lattices to complete inf-semilattices (cisls) using reference functions. Recently an auto-associative memory model based on a cisl was introduced by Sussner and Medeiros who conducted experiments concerning gray-scale image restoration using the median filter as a reference function. The adaptive median and Wiener filters often exhibit a better performance regarding noise reduction of corrupted images. We employ these filters as reference functions of auto-associative memories based on cisls in this paper. In experiments regarding the recall of noisy gray-scale images, our approach outperformed both the aforementioned image filters as well as a number of associative memory models including the cisl-based one that uses the median filter as a reference function.