A Classification of Critical Configurations for any Number of Projective
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Martin Bråtelund
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.