Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
复制标题
三角小波：具有六角对称性的各向同性图像表示
DOI：
10.1155/2009/248581
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发表时间：
2009
影响因子：
2.4
通讯作者：
O. Vasilyev
中科院分区：
文献类型：
--
作者：
K. Fujinoki;O. Vasilyev
本文介绍了三角小波，三角小波是定义在正三角格子上的二维不可分双正交小波。我们提出的结构是一维插值小波的简单不可分离扩展，然后是简单的概括。由此产生的三个定向高通滤波器对称地布置在晶格上，而低通滤波器具有六边形对称性，从而允许在三个细节分量均匀分布的意义上进行各向同性图像处理。将三角滤波器应用于图像，我们探索了与传统张量积变换相比真正受益于三角小波的应用。
This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. The resulting three oriented high-pass filters are symmetrically arranged on the lattice, while low-pass filters have hexagonal symmetry, thereby allowing an isotropic image processing in the sense that three detail components are distributed uniformly. Applying the triangular filter to images, we explore applications that truly benefit from the triangular wavelets in comparison with the conventional tensor product transforms.