The problem of structure from motion is concerned with recovering 3-dimensional structure of an object from a set of 2-dimensional images. Generally, all information can be uniquely recovered if enough images and image points are provided, but there are certain cases where unique recovery is impossible; these are called critical configurations. In this paper we use an algebraic approach to study the critical configurations for two projective cameras. We show that all critical configurations lie on quadric surfaces, and classify exactly which quadrics constitute a critical configuration. The paper also describes the relation between the different reconstructions when unique reconstruction is impossible.

翻译：运动恢复结构问题涉及从一组二维图像中恢复物体的三维结构。通常，若提供足够的图像和图像点，所有信息均可唯一恢复，但存在某些情况下无法实现唯一恢复；这些情况被称为关键配置。本文采用代数方法研究两个投影相机下的关键配置。我们证明所有关键配置均位于二次曲面上，并精确分类哪些二次曲面构成关键配置。本文还描述了当唯一重建不可行时不同重建结果之间的关系。