Generation of lattice independent vector sets for pattern recognition applications

Gonzalo Urcid-S.; Juan-Carlos Valdiviezo-N.

doi:10.1117/12.731925

17 September 2007 Generation of lattice independent vector sets for pattern recognition applications

Gonzalo Urcid-S., Juan-Carlos Valdiviezo-N.

Proceedings Volume 6700, Mathematics of Data/Image Pattern Recognition, Compression, Coding, and Encryption X, with Applications; 67000C (2007) https://doi.org/10.1117/12.731925
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

Lattice independence and strong lattice independence of a set of pattern vectors are fundamental mathematical properties that lie at the core of pattern recognition applications based on lattice theory. Specifically, the development of morphological associative memories robust to inputs corrupted by random noise are based on strong lattice independent sets, and real world problems, such as, autonomous endmember detection in hyperspectral imagery, use auto-associative morphological memories as detectors of lattice independence. In this paper, we present a unified mathematical framework that develops the relationship between different notions of lattice independence currently used in the literature. Computational procedures are provided to test if a given set of pattern vectors is lattice independent or strongly lattice independent; in addition, different techniques are fully described that can be used to generate sets of vectors with the aforementioned lattice properties.

Citation Download Citation

Gonzalo Urcid-S. and Juan-Carlos Valdiviezo-N. "Generation of lattice independent vector sets for pattern recognition applications", Proc. SPIE 6700, Mathematics of Data/Image Pattern Recognition, Compression, Coding, and Encryption X, with Applications, 67000C (17 September 2007); https://doi.org/10.1117/12.731925

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