Projective geometry is a mathematical framework in which to view computer vision in general, and especially image formation in particular. The main areas of application are those in which image formation and/or invariant descriptions between images are important, such as camera calibration, stereo, object recognition, scene reconstruction, mosaicing, image synthesis, and the analysis of shadows. This latter application arises from the fact that the composition of two perspective projections is not necessarily a perspective projection but is definitely a projective transformation; that is, projective transformations form a group, whereas perspective projections do not. Many areas of computer vision have little to do with projective geometry, such as texture analysis, color segmentation, and edge detection. And even in a field such as motion analysis, projective geometry offers little help when the rigidity assumption is lost because the relationship between projection rays in successive images cannot be described by such simple and elegant mathematics.
The following three sections contain the image formation equations, detailed derivations of the Essential and Fundamental matrices, and an interesting discussion of the interpretation of vanishing points.