Geometric symmetry in the quadratic Fisher discriminant operating on image pixels

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dc.creatorCaprari, Robert S.
dc.date2006-01-24
dc.date.accessioned2026-07-07T08:17:56Z
dc.date.available2026-07-07T08:17:56Z
dc.descriptionThis article examines the design of Quadratic Fisher Discriminants (QFDs) that operate directly on image pixels, when image ensembles are taken to comprise all rotated and reflected versions of distinct sample images. A procedure based on group theory is devised to identify and discard QFD coefficients made redundant by symmetry, for arbitrary sampling lattices. This procedure introduces the concept of a degeneracy matrix. Tensor representations are established for the square lattice point group (8-fold symmetry) and hexagonal lattice point group (12-fold symmetry). The analysis is largely applicable to the symmetrisation of any quadratic filter, and generalises to higher order polynomial (Volterra) filters. Experiments on square lattice sampled synthetic aperture radar (SAR) imagery verify that symmetrisation of QFDs can improve their generalisation and discrimination ability.
dc.descriptionAccepted for publication in IEEE Transactions on Information Theory
dc.identifierhttps://arxiv.org/abs/cs/0601102
dc.identifierhttp://arxiv.org/abs/cs/0601102
dc.identifierIEEE Transactions on Information Theory 52(4), April 2006, pp. 1780-1788
dc.identifierdoi:10.1109/TIT.2006.871581
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134262
dc.subjectInformation Theory
dc.subjectComputer Vision and Pattern Recognition
dc.titleGeometric symmetry in the quadratic Fisher discriminant operating on image pixels
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