I will present a new unifying theory of panoramic image formation covering all central omnidirectional sensors as well as any conventional pinhole camera. The model is based on a spherical projection followed by a projection from the sphere to the omnidirectional plane. The natural domain to process an omnidirectional signal is the sphere considered as a homogeneous space with the group action of rotation. By applying a Fourier transform on rotations we are able to obtain direct attitude information without point or line correspondences.

To describe more general mappings of omnidirectional planes we consider a new representation where the omnidirectional plane is lifted to a 3D circle space where transformations preserving points can be modeled as elements of the Lorentz group SO(3,1). Such a mapping models also the intrinsic geometry of an omnidirectional camera and it turns out that it drastically simplifies the problem of 3D-motion estimation. The additional robustness of of a huge field of view make such sensors irreplaceable in navigational tasks.