Kernel Computation in Morphological Associative Memories for Grayscale Image Recollection

G. Urcid (Mexico) and G.X. Ritter (USA)


Neural networks applications, morphological associativememory, non-boolean patterns, kernel, morphologicalstrong independence, minimax algebra.


Morphological associative memories (MAMs) form a sub class of morphological neural networks. Storage and recall in MAMs is realized using the matrix numerical operations of minimax algebra in a similar fashion as the classic corre lation encoding technique. The kernel method, based upon strong morphological independence of the exemplar pat tern set, allows to combine two MAMs for enhancing the recall capability when dealing with non-boolean patterns corrupted by random uniform noise. This paper describes a new procedure for assigning a kernel to any set of ex emplar patterns that are restricted to have non-negative entries over a finite set of values. Thus, our attention is fo cused to the specific case of grayscale images and we show, by means of illustrative examples, the recollection capabil ity of the kernel based morphological associative memory scheme including a probabilistic model for its performance.

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