(17) |

The converse of this result is that for a fixed viewpoint and pinhole , there is only one planar solution of the fixed viewpoint constraint equation. The unique solution is the perpendicular bisector of the line joining the pinhole to the viewpoint:

(18) |

(19) |

An immediate corollary of this result is that for a single fixed
pinhole, no two different planar mirrors can share the same viewpoint.
Unfortunately, a single planar mirror does not enhance the field of
view, since, discounting occlusions, the same camera moved from to and reflected in the mirror would have exactly the
same field of view. It follows that it is impossible to increase the
field of view by packing an *arbitrary number *of planar mirrors
(pointing in different directions) in front of a conventional imaging
system, while still respecting the fixed viewpoint constraint. On the
other hand, in applications such as stereo where multiple viewpoints
are a necessary requirement, the multiple views of a scene can be
captured by a single camera using multiple planar mirrors. See, for
example, [Goshtasby and Gruver, 1993] and [Nene and Nayar, 1998].

This brings us to the panoramic camera proposed by Nalwa [Nalwa, 1996]. To ensure a single viewpoint while using multiple planar mirrors, Nalwa [Nalwa, 1996] arrived at a design that uses four separate imaging systems. Four planar mirrors are arranged in a square-based pyramid, and each of the four cameras is placed above one of the faces of the pyramid. The effective pinholes of the cameras are moved until the four effective viewpoints (i.e. the reflections of the pinholes in the mirrors) coincide. The result is a sensor that has a single effective viewpoint and a panoramic field of view of approximately . The panoramic image is of relatively high resolution since it is generated from the four images captured by the four cameras. This sensor is straightforward to implement, but requires four of each component: i.e. four cameras, four lenses, and four digitizers. (It is possible to use only one digitizer but at a reduced frame rate.)