ABSTRACT
Morphological Associative Memories (MAM’s) have been used in two different ways: a direct approach which is suitable for input patterns containing either dilative or erosive noise and an indirect one for arbitrarily corrupted input patterns which is based on kernel vectors. Although kernel vectors represent an elegant representation for the retrieval of arbitrarily corrupted patterns they severely suffer from noise, especially when this noise affects one or more points of the input pattern corresponding to respective kernel points. In this paper, a theoretical proof of this observation is established and a new kernel definition is proposed which is more robust to noise than the traditional kernel vectors. The new kernels are not binary but they contain elements with values in the interval [0, 1], where each selected kernel value is related to the frequency and the position of the respective elements of the training patterns. The performance of the new method is also demonstrated by simulation examples.
