The problem of structure from motion is concerned with recovering the 3-dimensional structure of an object from a set of 2-dimensional images taken by unknown cameras. Generally, all information can be uniquely recovered if enough images and point correspondences are provided, yet there are certain cases where unique recovery is impossible; these are called \emph{critical configurations}. We use an algebraic approach to study the critical configurations for three projective cameras. We show that all critical configurations lie on the intersection of quadric surfaces, and classify exactly which intersections constitute a critical configuration.
翻译:运动的结构问题涉及从一组由未知相机拍摄的二维图像中恢复一个对象的三维结构。 一般而言,如果提供了足够的图像和点对应信息,所有信息都可以被独一地恢复,但有些情况下无法实现独特的恢复;这些被称为 emph{ 关键配置} 。 我们使用代数法来研究三个投影相机的关键配置。 我们显示所有关键配置都位于四重表面的交叉点上, 并精确地区分哪些交叉点构成关键配置 。