Multi-View Geometry for General Camera Models

Abstract

We consider the structure-from-motion problem for a highly general imaging model where cameras are modeled as possibly unconstrained sets of projection rays. This allows to describe most existing camera types, including pinhole cameras, sensors with radial or more general distortions, catadioptric cameras (central or non-central), etc. We introduce a hierarchy of general camera models: the most general model has unconstrained projection rays whereas the most constrained model dealt with here is the central model, where all rays pass through a single point. Intermediate models are what we call axial cameras (all rays touch a single line), and x-slit cameras (rays touch two lines). The foundations for a multi-view geometry of completely non-central cameras are given, leading to the formulation of multi-view matching tensors, analogous to the fundamental/essential matrices, trifocal and quadrifocal tensors of perspective cameras. This framework is then specialized explicitly for the two-view case, for the intermediate camera types mentioned above.