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.

中文翻译：

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球体上的筛选卷积

通过球体上狄拉克三角洲的筛选特性定义了一种新的球面卷积。所谓的筛选卷积是由一个函数与另一个函数的翻译版本的内积定义的，但在球体上采用了替代翻译算子。当在调和空间中观察时，该平移算子与欧几里得平移类似。筛选卷积满足了替代定义中缺乏的各种理想特性，即：它支持定向核；它有一个保留在球体上的输出；并且计算效率高。地球地形图上的筛选卷积图示表明，它支持定向内核以执行各向异性过滤，而其输出仍保留在球体上。