论文标题
在球体上筛选卷积
Sifting Convolution on the Sphere
论文作者
论文摘要
通过在球体上迪拉克三角洲的筛分特性来定义一种新型的球形卷积。所谓的筛选卷积是由一个函数的内部产物和另一个函数的内部产物定义的，但在球体上采用了替代翻译运算符。当在谐波空间中查看时，该翻译操作员与欧几里得翻译相似。筛分卷积满足了替代定义中缺少的各种理想特性，即：它支持定向内核；它的输出保留在球体上。并有效地计算。地球地形图上的筛分卷积的例证表明，它支持方向内核进行各向异性滤波，而其输出仍保留在球体上。
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the adoption of an alternative translation operator on the sphere. This translation operator follows by analogy with the Euclidean translation when viewed in harmonic space. The sifting convolution satisfies a variety of desirable properties that are lacking in alternate definitions, namely: it supports directional kernels; it has an output which remains on the sphere; and is efficient to compute. An illustration of the sifting convolution on a topographic map of the Earth demonstrates that it supports directional kernels to perform anisotropic filtering, while its output remains on the sphere.
