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Reconstruction of Patterns from Noisy Inputs Using Morphological Associative Memories

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Abstract

Morphological neural networks are based on a new paradigm for neural computing. Instead of adding the products of neural values and corresponding synaptic weights, the basic neural computation in a morphological neuron takes the maximum or minimum of the sums of neural values and their corresponding synaptic weights. By taking the maximum (or minimum) of sums instead of the sum of products, morphological neuron computation is nonlinear before thresholding. As a consequence, the properties of morphological neural networks are drastically different than those of traditional neural network models. In this paper we restrict our attention to morphological associative memories. After a brief review of morphological neural computing and a short discussion about the properties of morphological associative memories, we present new methodologies and associated theorems for retrieving complete stored patterns from noisy or incomplete patterns using morphological associative memories. These methodologies are derived from the notions of morphological independence, strong independence, minimal representations of patterns vectors, and kernels. Several examples are provided in order to illuminate these novel concepts.

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Authors and Affiliations

  1. Center for Computer Vision and Visualization, University of Florida, Gainesville, Florida, 32611-6120, USA

    Gerhard X. Ritter, Gonzalo Urcid & Laurentiu Iancu

  2. Optics Department, INAOE, Tonantzintla, Pue, 72000, Mexico

    Gonzalo Urcid

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  1. Gerhard X. Ritter
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  2. Gonzalo Urcid
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  3. Laurentiu Iancu
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Ritter, G.X., Urcid, G. & Iancu, L. Reconstruction of Patterns from Noisy Inputs Using Morphological Associative Memories. Journal of Mathematical Imaging and Vision 19, 95–111 (2003). https://doi.org/10.1023/A:1024773330134

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