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Structure from motion is the process of recovering information about camerasand 3D scene from a set of images. Generally, in a noise-free setting, allinformation can be uniquely recovered if enough images and image points areprovided. There are, however, certain cases where unique recovery isimpossible, even in theory; these are called critical configurations. We use arecently developed algebraic approach to classify all critical configurationsfor any number of projective cameras. We show that they form well-knownalgebraic varieties, such as quadric surfaces and curves of degree at most 4.This paper also improves upon earlier results both by finding previouslyunknown critical configurations and by showing that some configurationspreviously believed to be critical are in fact not.

A Classification of Critical Configurations for any Number of Projective Views