Triangular biorthogonal Wavelets with Extended Lifting
Triangular biorthogonal Wavelets with Extended Lifting
复制标题
具有扩展提升的三角双正交小波
DOI：
10.1142/s0219691313600023
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
S. Ishimitsu
中科院分区：
文献类型：
--
作者：
K. Fujinoki;S. Ishimitsu
我们通过引入一个新的操作来推广二维提升，我们称之为扭转，给出了一个新的三角形双正交小波族，它是在三角形晶格上定义的。所得到的滤波器继承了早期三角双正交小波滤波器的几个显著特征，如低通滤波器的六边形对称性，三个高通滤波器在晶格上的对称排列，以及小波分解在三个细节分量上产生均匀的能量分布，保持了分解图像的各向同性。此外，这些滤波器是真正不可分离的二维小波滤波器的双正交集合，具有更大的支持，它为分解图像的三个细节组件提供了更大的总能量。我们表明，这在提取图像的边缘结构时起着至关重要的作用。
We present a new family of triangular biorthogonal wavelets that is defined on a triangular lattice by introducing a new operation to generalize two-dimensional lifting, which we call twist. The resulting filters inherit several remarkable features of the early triangular biorthogonal wavelet filters such as the hexagonal symmetry of low-pass filters, symmetrical arrangement of three high-pass filters on the lattice, and that the wavelet decomposition produces uniform energy distributions over three detail components, preserving the isotropy of decomposed images. Additionally, these filters are a biorthogonal set of truly nonseparable two-dimensional wavelet filters that have much larger support, which provides much larger portions of the total energy to three detail components of decomposed images. We show that this plays a crucial role when extracting the edge structure of an image.