Nonlinear Projections - Transformations and Projections in Computer Graphics - page 186

Note : The pinhole used to be the first camera of many a poor youngster. This
is simply a box with a small hole in front and film or light-sensitive paper loaded in
back. The shutter can be as simple as a piece of tape that's removed to expose the film,
then reapplied manually, or it can be a purchased, cable-operated shutter assembly. If
the hole is small enough, the resulting image is sharp; if the film is wide, this primitive
device can produce wide-angle images.
The total photograph . We now turn to a completely different approach to
the problem of creating a panorama with a camera. This approach, termed by its
inventor the total photograph , was developed and patented by Dick Termes in 1980
and is described in [Termes 80]. To understand this technique, consider the cubic
panoramic projections of Section 4.7. We imagine an observer located at the center of
a cube (Figure 4.30a) and looking at the three-dimensional scene outside. Everything
the observer sees is etched on the sides of the cube or is painted there by the observer.
Given a three-dimensional scene and a camera, the problem is to generate such a cube.
In general, we want a method where we can project a scene on the sides of any of the
five regular polyhedra, as discussed in Section 4.9.
The first step is to decide what regular polyhedron we want. For example, we may
want to create a panorama on the 20 triangular sides (or faces) of an icosahedron. We
use suitable material, such as wood, plastic, or metal, to construct a solid icosahedron
and mount it on a good-quality, stable camera tripod. (The tripod may have to be
loaded with extra weight to make it extremely stable.) The icosahedron stays fixed
while pictures are taken. We drill small holes (labeled #34 in Figure 4.39) in each of
the 20 sides of the icosahedron to enable us to quickly attach a special bracket to any
side. A camera is mounted on the bracket. (The camera has to have a wide field of view,
so pictures taken from adjacent faces of the polyhedron do overlap). We then place the
bracket with the camera in one of the 20 sides of the icosahedron and, while holding it
stable in our hand, take a snapshot. This guarantees that the center of the camera lens
is right over the center of the polygon face. It is also important to make sure that the
camera's line of sight is perpendicular to the polygon face. We repeat this for the 19
remaining sides to end up with 20 pictures, each showing what a viewer located on that
face of the icosahedron would see.
Figure 4.39 is taken from the patent application. The first five figures show the
five Platonic solids, each with two holes on each face, for quick mounting of the bracket.
Part 6 of the figure shows the bracket, part 7 shows a camera mounted on the bracket,
andpart8isanexplodedviewofanicosahedronmountedonacameratripodandthe
bracket mounted on one side.
The only problem is that the camera is located outside the icosahedron, not inside.
Thus, the camera sees more than an inside observer would see through each face. The
20 photographs therefore partially overlap and we need to identify the overlapping parts
and remove them. The result should be 20 triangular pictures, each corresponding to
what an observer inside the icosahedron would see through one face. These triangles
can then be pasted together to form an actual icosahedron.
Figure 4.40 illustrates this process. Two partially overlapping pictures are placed
such that the overlapping parts match precisely (part 9). The centers of the pictures
are then identified and connected by a straight segment (#56 in part 10), and another