Critical Configurations: A classification of all critical configurations for any number of projective views
Martin Bråtelund · NORA - Norwegian Open Research Archives · 2024
“Structure from motion” is the process of recovering cameras and a 3D scene from a set of images. Usually, all information can be recovered if enough images and image points are provided. There are, however, certain cases where the shape of the 3D scene and the positions of the cameras are such that a recovery is impossible, even in theory; these cases are called "critical configurations". My work classifies all critical configurations for any number of projective cameras. I show that they form well-known algebraic varieties, such as quadratic surfaces and curves of degree at most four. My work also improves upon earlier results, both by finding critical configurations that were previously unknown and by showing that some configurations that were believed to be critical are in fact not. While the techniques developed to make this classification can help make similar classifications in other theoretical settings, the classification result itself has real-world application. Algorithms recovering 3D information from images are already in use, for instance in manufacturing, healthcare, and transportation. A property of critical configurations is that reconstruction algorithms tend to become unstable if the 3D-scene approximates a critical configuration. Hence, understanding critical configurations is key to avoiding such difficulties.