标题： 公共线的半代数几何 显示英文标题

标题： Semi-algebraic geometry of common lines

摘要： 冷冻电子显微镜是结构生物学中用于发现/确定小分子三维结构的技术。 此过程中的关键步骤是检测未知嵌入图像平面之间的公共交线。 我们从实验中检测到的未嵌入几何数据的角度出发，对这些公共交线进行内在表征。 我们证明这些公共交线形成一个半代数集，即它们由多项式等式和不等式定义。 这些多项式次数较低，并且利用球面几何的技术，我们在本文中显式地推导了它们。 显示英文摘要

摘要： Cryo-electron microscopy is a technique in structural biology for discovering/determining the 3D structure of small molecules. A key step in this process is detecting common lines of intersection between unknown embedded image planes. We intrinsically characterize such common lines in terms of the unembedded geometric data detected in experiments. We show these common lines form a semi-algebraic set, i.e., they are defined by polynomial equalities and inequalities. These polynomials are low degree and, using techniques from spherical geometry, we explicitly derive them in this paper.