Critical configurations for two projective views, a new approach

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.