Master Thesis - Fachbereich Informatik

2.1. VISUAL MEASUREMENTS 13
Figure 2.4: Thin lens camera model.
Any ray entering the lens parallel to the axis on one side goes through the focus on
the other side
Any ray entering the lens from the focus on one side emerges parallel to the axis on
the other side
The geometry of a thin lens imaging system is shown in Figure 2.4. F and ˆ F are the
focus points before and behind the lens. From this model one can derive the fundamental
equation of thin-lenses [65]:
1 1 1
+ = (2.5)
Z z f
where Z is the distance or depth of a point to the lens and z the distance between the
lens and the image plane. The focal length f, i.e. the distance between the focus point
and the lens is equal at both sides of the thin lens in the ideal model.
Thick Lens Camera Real lenses are represented much better by a thick lens model. The
thin lens model does not consider several aberrations that come with real lenses. This
includes defocusing of rays that are neither parallel nor go through the focus (spherical
aberration), different refraction based on the wavelength or color of light rays entering
the lens (chromatic aberration), or focusing of objects at different depths. Another factor
that is important with real lenses with respect to accurate measuring applications, is lens
distortion. Ideally, a world point, its image point and the optical center are collinear, and
world lines are imaged as lines [30]. For real cameras this model does not hold. Especially
at the image boundaries, straight lines appear curved (radial distorted). The effect of
distortion will be re-addressed in following sections.
2.1.4. Camera Calibration
Until now, all relationships between 3D points and image coordinates have been defined
with respect to a common (camera) reference frame. Usually, the location of a point
in the world is not known in camera coordinates. Thus, if one wants to relate world
coordinates to image coordinates, or vice versa, one has to consider geometric models and