Image formation

The basic camera model is a pinhole camera, though the real-world cameras that we use are far more complex models. A pinhole camera is made up of a very small slit on a plane that allows the formation of an image as depicted in the following figure:

This camera converts a point in the physical world, often termed the real world, to a pixel on an image plane. The conversion follows the transformation of the three-dimensional coordinate to two-dimensional coordinates. Here in the image plane, the coordinates are denoted as where

, P_i is any point on an image. In the physical world, the same point is denoted by

, where P_w is any point in the physical world with a global reference frame.  

P_i(x', y') and P_w(x, y, z) can be related as, for an ideal pin hole camera:

Here, f is focal length of the camera. 

For further discussion on geometry of image formation, it is necessary to introduce the homogeneous coordinate system. The physical world coordinate system is referred to as Euclidean...