Morphological associative memories (MAMs) use a lattice algebra approach to store and recall pattern associations. The lattice matrix operations endow MAMs with properties that are completely different than those of traditional associative memory models. In the present paper, we focus our attention to morphological bidirectional associative memories (MBAMs) capable of storing and recalling non-boolean patterns degraded by random noise. The notions of morphological strong independence (MSI), minimal representations, and kernels are extended to provide the foundation of bidirectional recall when dealing with noisy inputs. For arbitrary pattern associations, we present a practical solution to compute kernels in MBAMs by induced MSI.
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