We present here a comprehensive imaging theory about cone mirrors in a single-view-point (SVP) configuration and show that an SVP cone mirror catadioptric system is not only practical but also has unique advantages for certain applications. We show its merits and weaknesses and how to build a workable system.

Autonomous robots need to acquire both omnidirectional view and stereo in real-time without sacrificing too much image resolution. The recent catadioptric omni-directional vision sensors provide simple affordable real-time omni-directional images but only at the cost of rather low image resolutions. This work describes a novel omni-directional stereo image sensor providing the highest resolution while still retaining the simplicity and real-time advantages that are unique to the family of catadioptric sensors. Only one simple reflective surface, a beam splitter and two regular (perspective) cameras are needed.

Pinhole camera model is a simplified subset of geometric optics. In special cases like the image formation of the cone (a degenerate conic section) mirror in an omnidirectional view catadioptric system, there are more complex optical phenomena involved that the simple pinhole model can not explain. We show that using the full geometric optics model a true single viewpoint cone mirror omni-directional system can be built. We show how such a system is built first, and then show in detail how each optical phenomenon works together to make the system true single viewpoint. The new system requires only simple off-the-shelf components and still outperforms other single viewpoint omni-systems for many applications.

This paper proposes a new approach to resolve the ambiguity problem in multistriping laser triangulation systems. Our approach is based on the Fourier slice theorem which is briefly described in this paper. This theorem also forms the basis of X-ray CT (computed tomography) reconstruction.