A Classification of Critical Configurations for any Number of Projective Views
This addresses a foundational theoretical problem in computer vision for researchers and practitioners, providing a complete classification that clarifies ambiguities in 3D reconstruction, though it is incremental as it builds on existing algebraic methods.
The paper tackles the problem of identifying critical configurations in structure from motion where unique 3D reconstruction is impossible, using an algebraic approach to classify all such configurations for any number of projective cameras, showing they form known algebraic varieties like quadrics and curves up to degree 4, and improves earlier results by finding new configurations and correcting previous beliefs.
Structure from motion is the process of recovering information about cameras and 3D scene from a set of images. Generally, in a noise-free setting, all information can be uniquely recovered if enough images and image points are provided. There are, however, certain cases where unique recovery is impossible, even in theory; these are called critical configurations. We use a recently developed algebraic approach to classify all critical configurations for any number of projective cameras. We show that they form well-known algebraic varieties, such as quadric surfaces and curves of degree at most 4. This paper also improves upon earlier results both by finding previously unknown critical configurations and by showing that some configurations previously believed to be critical are in fact not.