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Machine Vision and Applications

Erschienen in:

01.11.2016 | Special Issue Paper

Pattern recognition in multilinear space and its applications: mathematics, computational algorithms and numerical validations

verfasst von: Hayato Itoh, Atsushi Imiya, Tomoya Sakai

Erschienen in: Machine Vision and Applications | Ausgabe 8/2016

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Abstract

We clarify the mathematical equivalence between low-dimensional singular value decomposition and low-order tensor principal component analysis for two- and three-dimensional images. Furthermore, we show that the two- and three-dimensional discrete cosine transforms are, respectively, acceptable approximations to two- and three-dimensional singular value decomposition and classical principal component analysis. Moreover, for the practical computation in two-dimensional singular value decomposition, we introduce the marginal eigenvector method, which was proposed for image compression. For three-dimensional singular value decomposition, we also show an iterative algorithm. To evaluate the performances of the marginal eigenvector method and two-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for six datasets of two-dimensional image patterns. To evaluate the performances of the iterative algorithm and three-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for datasets of gait patterns and human organs. For two- and three-dimensional images, the two- and three-dimensional discrete cosine transforms give almost the same recognition rates as the marginal eigenvector method and iterative algorithm, respectively.

Vorheriger Artikel Two-stage approach to extracting visual objects from paper documents

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Titel: Pattern recognition in multilinear space and its applications: mathematics, computational algorithms and numerical validations
verfasst von: Hayato Itoh
Atsushi Imiya
Tomoya Sakai
Publikationsdatum: 01.11.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Machine Vision and Applications / Ausgabe 8/2016
Print ISSN: 0932-8092
Elektronische ISSN: 1432-1769
DOI: https://doi.org/10.1007/s00138-016-0806-2

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