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Lattice Algebra Approach to Color Image Segmentation

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Abstract

This manuscript describes a new technique for segmenting color images in different color spaces based on geometrical properties of lattice auto-associative memories. Lattice associative memories are artificial neural networks able to store a finite set X of n-dimensional vectors and recall them when a noisy or incomplete input vector is presented. The canonical lattice auto-associative memories include the min memory W XX and the max memory M XX , both defined as square matrices of size n×n. The column vectors of W XX and M XX , scaled additively by the components of the minimum and maximum vector bounds of X, are used to determine a set of extreme points whose convex hull encloses X. Specifically, since color images form subsets of a finite geometrical space, the scaled column vectors of each memory will correspond to saturated color pixels. Thus, maximal tetrahedrons do exist that enclose proper subsets of pixels in X and such that other color pixels are considered as linear mixtures of extreme points determined from the scaled versions of W XX and M XX . We provide illustrative examples to demonstrate the effectiveness of our method including comparisons with alternative segmentation methods from the literature as well as color separation results in four different color spaces.

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Authors and Affiliations

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

    Gonzalo Urcid & Juan-Carlos Valdiviezo-N.

  2. CISE Department, University of Florida, Gainesville, FL, 32611-6120, USA

    Gerhard X. Ritter

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  1. Gonzalo Urcid
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  2. Juan-Carlos Valdiviezo-N.
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  3. Gerhard X. Ritter
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Correspondence to Gonzalo Urcid.

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Urcid, G., Valdiviezo-N., JC. & Ritter, G.X. Lattice Algebra Approach to Color Image Segmentation. J Math Imaging Vis 42, 150–162 (2012). https://doi.org/10.1007/s10851-011-0302-2

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