In this paper we study the formal algebraic structure underlying the intrinsic classification algorithm, recently introduced in Singer et al. (SIAM J. Imaging Sci. 2011, accepted), for classifying noisy projection images of similar viewing directions in three-dimensional cryo-electron microscopy (cryo-EM). This preliminary classification is of fundamental importance in determining the three-dimensional structure of macromolecules from cryo-EM images. Inspecting this algebraic structure we obtain a conceptual explanation for the admissibility (correctness) of the algorithm and a proof of its numerical stability. The proof relies on studying the spectral properties of an integral operator of geometric origin on the two-dimensional sphere, called the localized parallel transport operator. Along the way, we continue to develop the representation theoretic set-up for three-dimensional cryo-EM that was initiated in Hadani and Singer (Ann. Math. 2010, accepted).

中文翻译：

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三维冷冻电子显微镜中的表示理论模式 II - 类平均问题。

在本文中，我们研究了 Singer 等人最近引入的内在分类算法的形式代数结构。（SIAM J. Imaging Sci. 2011，已接受），用于对三维冷冻电子显微镜 (cryo-EM) 中相似观察方向的噪声投影图像进行分类。这种初步分类对于从冷冻电镜图像中确定大分子的三维结构至关重要。通过检查这个代数结构，我们获得了算法可接受性（正确性）的概念解释及其数值稳定性的证明。该证明依赖于研究二维球体上几何原点积分算子的谱特性，称为局部平行输运算子。一路上，