Critical configurations for two projective views, a new approach
This work addresses a fundamental issue in computer vision for researchers and practitioners, offering a theoretical classification that is incremental to existing knowledge.
The paper tackles the problem of identifying critical configurations in structure from motion for two projective cameras, showing that all such configurations lie on quadric surfaces and providing a classification of these quadrics.
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.