ABSTRACT
In Chapters 2-7, we focused on the geometry of lines and planes, to which we added spheres and circles in Chapter 8 and considered their conformal transformations. Conformal transformations include familiar mappings such as translation, rotation, and scale change that frequently appear in many engineering applications, but inversion is a unique mapping involving spheres and circles. In this chapter, we consider camera imaging geometry as a typical geometric problem that involves inversion. First, we describe conventional perspective projection cameras. Then, we turn to fisheye lens cameras. We further analyze the imaging geometry of omnidirectional cameras that use parabolic mirrors. We show that inversion with respect to a sphere plays an essential role in all such cameras. We further describe how we can obtain 3D interpretation of a scene from omnidirectional camera images, and its imaging geometry is compared with those of cameras that use hyperbolic and elliptic mirrors.
