Master Thesis - Fachbereich Informatik

2.1. VISUAL MEASUREMENTS 11
(a)
Figure 2.2: Parallel lines intersect at horizon at perspective. Image taken by F. Wagenfeld
at Alaska Highway between Watson Lake and Whitehorse, Canada.
In the 15th century, Filippo Brunelleschi used the pin hole camera model to demonstrate
the laws of perspective discovered earlier [24, 38]. Two main effects characterize the pin
hole perspective or central perspective:
Close objects appear larger than far ones
Parallel lines intersect at horizon
Figure 2.2 visualizes these effects of perspective at an example.
A drawback of the pinhole camera with respect to practical use in combination with a
photosensitive device is its long exposure time, since only a little amount of light enters
the image plane at one time [65]. However, the pinhole model can be used to derive
fundamental properties in a mathematical sense that describe the imaging process. These
properties can be extended by more realistic models to imply real imaging devices.
Figure 2.3(a) gives an overview over the pinhole geometry. The camera center O, also
denoted as optical center or center of projection, is the origin of a 3D coordinate system
with the axis X, Y and Z. This 3D coordinate system is denoted as camera reference
frame or simply camera frame. The image plane ΠI is defined to be parallel to the XY
plane, i.e. perpendicular to the Z axis. The point o where the Z axis intersects the image
planeisreferredtoasimage center. TheZ axis, i.e. the line through O and o is denoted
as optical axis.
The fundamental equations of a perspective camera describe the relationship between
apointP =(X, Y, Z) T in the camera frame and a point p =(x, y) T in the image plane:
x = f X
Z
y = f Y
Z
(2.1)
(2.2)
where f is the focal length of the camera. p can be seen as the point of intersection of a
line through P and the center of projection with the image plane ΠI [30]. This relationship
can be easily derived from Figure 2.3(b). In the following, lower-case letters will always