球面上的筛选卷积
Sifting Convolution on the Sphere
AI总结：
针对球面卷积缺乏方向核、输出脱离球面或计算低效的问题，本文利用 Dirac delta 的筛选性质提出筛选卷积，并通过地球地形图验证其各向异性滤波能力。
摘要：
本文利用球面上 Dirac delta 函数的筛选性质，定义了一种新颖的球面卷积。所谓筛选卷积由一个函数与另一个函数的平移版本的内积定义，但采用了球面上的另一种平移算子。从调和空间观察时，该平移算子可类比欧氏平移得到。筛选卷积满足其他替代定义所缺乏的多种理想性质，即：它支持方向核；其输出仍位于球面上；并且计算高效。在地球地形图上对筛选卷积的演示表明，它支持方向核执行各向异性滤波，同时其输出仍位于球面上。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
