General models for rational cameras and the case of two-slit projections

The rational camera model recently introduced in [18] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry. This paper provides a concrete embedding of rational cameras explicitly accounting for the mapping between physical visual rays and image points, missing in the original model. This allows us to derive simple but general analytical expressions for direct and inverse projections, and define primitive rational cameras equivalent under the action of various projective transformations, leading to a generalized notion of intrinsic coordinates in this setting. The methodology is general, but it is illustrated concretely by an in-depth study of two-slit cameras, which we describe using a pair of linear projections. This simple analytical form allows us to describe models for the corresponding primitive cameras, to introduce intrinsic parameters with a clear geometric meaning, and to define an epipolar tensor characterizing two-view correspondences. In turn, this leads to new algorithms for structure from motion and self-calibration.