Since Euclidean geometry describes our world so well, it is at first tempting to think that it is the only type of geometry. Euclidean geometry is actually a subset of what is known as projective geometry . To see the relationships between these different geometries, consult Figure 1. Projective geometry models well the imaging process of a camera because it allows a much larger class of transformations than just translations and rotations, a class which includes perspective projections. The four different geometries, the transformations allowed in each, and the measures that remain invariant under those transformations.
Projective geometry exists in any number of dimensions, just like Euclidean geometry.
That section presents many concepts which are useful in understanding the image plane and which have analogous concepts in . The final section then briefly discusses the relevance of projective geometry to computer vision, including discussions of the image formation equations and the Essential and Fundamental matrices. The purpose of this monograph will be to provide a readable introduction to the field of projective geometry and a handy reference for some of the more important equations. The first-time reader may find some of the examples and derivations excessively detailed, but this thoroughness should prove helpful for reading the more advanced texts, where the details are often omitted.