An Enhanced Unified Camera Model

This paper describes a novel projection model based on the so-called unified projection model. The new model applies to catadioptric systems and wide-angle fish-eye cameras, it does not require additional mapping to model distortions, and it takes just two projection parameters more than a simple pinhole model to represent radial distortion (one parameter more than the unified model). Here, we provide a study of different mathematical aspects of the model, its application limits, and explicit closed-form inversion. The latter allows to apply all the notions of epipolar geometry with no difficulties. Also, we introduce a concept of projection surface, which is a useful notion to study and compare different projection models with radial distortion. Using developed software, several different lenses were calibrated using the proposed model, and in all cases, subpixel precision was achieved.