Reconstruction from Projections

In chapter 2 we discussed in detail how a discrete two-dimensional image is formed from a three-dimensional scene by an optical system. In this chapter we discuss the inverse process, the reconstruction of a three-dimensional scene from two-dimensional projections. Reconstruction from only one projection is an underdetermined inverse problem which generally shows an infinite number of solutions. As an illustration, figure 13.1 shows the perspective projection of a bar onto an image plane. We will obtain identical projections at the image plane, whenever the endpoints of a bar lie on the same projection beams. Even if the bar shows a curvature in the projection plane, we will still see a straight line at the image plane.