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首页> 外文期刊>IEEE Transactions on Information Theory >Geometric symmetry in the quadratic fisher discriminant operating on image pixels
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Geometric symmetry in the quadratic fisher discriminant operating on image pixels

机译：对图像像素进行二次Fisher判别的几何对称性

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摘要

This correspondence 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 symmetrization of any quadratic filter, and generalizes to higher order polynomial (Volterra) filters. Experiments on square lattice sampled synthetic aperture radar (SAR) imagery verify that symmetrization of QFDs can improve their generalization and discrimination ability.
机译：该对应关系检查了当图像集合包含不同样本图像的所有旋转和反射版本时，直接对图像像素进行操作的二次费舍尔判别式（QFD）的设计。设计了一种基于群论的程序来识别和丢弃任意采样格中由于对称而变得多余的QFD系数。该过程引入了简并矩阵的概念。建立方格点组（8倍对称性）和六角格点组（12倍对称性）的张量表示。该分析在很大程度上适用于任何二次滤波器的对称化，并推广到高阶多项式（Volterra）滤波器。在方格采样合成孔径雷达（SAR）图像上进行的实验证明，QFD的对称化可以提高其泛化和判别能力。

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