Critical configurations for three projective views
This addresses a fundamental issue in computer vision for researchers and practitioners, but it is incremental as it builds on prior work on critical configurations.
The paper tackles the problem of identifying critical configurations in structure from motion where 3D recovery from 2D images is impossible, showing that all such configurations for three projective cameras lie on intersections of quadric surfaces and providing a classification of these intersections.
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 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.