Most Structure from Motion (linear *and* non-linear) techniques
begin by assuming a perspective projection model as shown in
Figure 3 which can be traced back to
Durer and Renaissance painters. Alternative projection models include
paraperspective or orthographic cases. Here, three 3D feature points
are projecting onto an image plane ()
with perspective rays
originating at the *center of projection* (COP), which would lie
within the physical camera. The origin of the coordinate system is
traditionally taken to be the COP and the *focal length*, ** f** is
the distance from the COP to the image plane along the

Applying Thales theorem, we obtain the perspective projection formula
as in Equation 1. Typically, the focal length ** f** is
set to 1 to simplify the expression since, in this model,

This perspective projection is often referred to as a pinhole
camera. Although the focal length is the most emphasized internal
camera geometry parameter, there exist more complex full
parameterizations. In fact, real cameras have many other internal
geometry variables. A more complete camera parameterization is shown in
Equation 2 [41]. Here,
the ** K** matrix includes