In this paper, we propose a new approach for symbol recognition using structural signatures and a Galois lattice as a classifier. The structural signatures are based on topological graphs computed from segments which are extracted from the symbol images by using an adapted Hough transform. These structural signatures-that can be seen as dynamic paths which carry high-level information-are robust toward various transformations. They are classified by using a Galois lattice as a classifier. The performance of the proposed approach is evaluated based on the GREC'03 symbol database, and the experimental results we obtain are encouraging.
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http://dx.doi.org/10.1109/TSMCB.2011.2108646 | DOI Listing |
Phys Rev Lett
March 2020
Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium.
We provide a generalization of the matrix product operator formalism for string-net projected entangled pair states (PEPS) to include nonunitary solutions of the pentagon equation. These states provide the explicit lattice realization of the Galois conjugated counterparts of (2+1)-dimensional topological quantum field theories, based on tensor fusion categories. Although the parent Hamiltonians of these renormalization group fixed point states are gapless, these states can still be the topological ground states of a gapped non-Hermitian Hamiltonian.
View Article and Find Full Text PDFScientificWorldJournal
June 2015
College of Science, Xi'an Shiyou University, Xi'an 710065, China.
In this paper, we mainly investigate the equivalence between multigranulation approximation space and single-granulation approximation space from the lattice-theoretic viewpoint. It is proved that multigranulation approximation space is equivalent to single-granulation approximation space if and only if the pair of multigranulation rough approximation operators [Formula in text] forms an order-preserving Galois connection, if and only if the collection of lower (resp., upper) definable sets forms an (resp.
View Article and Find Full Text PDFIEEE Trans Syst Man Cybern B Cybern
August 2011
In this paper, we propose a new approach for symbol recognition using structural signatures and a Galois lattice as a classifier. The structural signatures are based on topological graphs computed from segments which are extracted from the symbol images by using an adapted Hough transform. These structural signatures-that can be seen as dynamic paths which carry high-level information-are robust toward various transformations.
View Article and Find Full Text PDFMath Biosci
July 2006
Research Institute of Tropical Roots, Tuber Crops, Bananas and Plantains (INIVIT), Biotechnology Group, Cuba.
Starting from the four DNA bases order in the Boolean lattice, a novel Lie Algebra of the genetic code is proposed. Here, the main partitions of the genetic code table were obtained as equivalent classes of quotient spaces of the genetic code vector space over the Galois field of the four DNA bases. The new algebraic structure shows strong connections among algebraic relationships, codon assignments and physicochemical properties of amino acids.
View Article and Find Full Text PDFBehav Genet
March 2001
FRE CNRS 2134 Génétique, Neurogénétique Comportement, Institut de Transgénose, Orleans.
In order to develop a genetic study of human laterality, we conducted an exploratory study concerning one aspect of this phenotype: lattice analysis was used to determine whether the structure of manual preference was the same for right- and left-handers. The study highlights the links between two sets - participants and actions - describing binary data, by ordering them "dually" along a "Galois lattice": participants were ordered according to subsets of actions for which they used only their writing hand, while actions were ordered according to sub-groups using their writing hand to perform them. The twelve item questionnaire of Annett was analysed in two samples of 94 adult right-hand and 31 left-hand writers.
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