Master Thesis - Fachbereich Informatik

2. Technical Background
2.1. Visual Measurements
This section introduces the basic concepts and techniques making visual measurements
possible. It is elementary to understand the fundamental process of image acquisition
as well as the underlying camera models and geometries to be able to understand what
parameters influence the measurement of real world objects in video images. Based on
these concepts one can determine the factors that influence accuracy and precision.
Extracting information about real world objects from images in machine vision applications
is closely related to the area of photogrammetry. In [5], photogrammetry is defined
as the art, science, and technology of obtaining reliable information about physical objects
and the environment through the processes of recording, measuring, and interpreting photographic
images and patterns of electromagnetic radiant energy and other phenomena.
There are many traditional applications of photogrammetry in geography, remote sensing,
medicine, archaeology, or crime detection. In machine vision applications, there is a
wide range of measuring tasks including dimensional measuring (size, distance, diameter,
etc.) or angles. Although sophisticated algorithms can increase accuracy, the quality and
repeatability of measurements is always related to the hardware used (e.g. camera sensor,
optical system, digitizer) as well as the environmental conditions (e.g. illumination).
2.1.1. Accuracy and Precision
Throughout this thesis the terms accuracy and precision are used quite often and are
mostly related to measuring quality. Although these terms may be used synonymously in
a different context, with respect to measurements they have a very distinct meaning.
Accuracy relates a measured length to a known reference truth or ground truth. The
closer a measurement approximates the ground truth, the more accurate is the measuring
system. Precision represents the repeatability of measurements, i.e. how much different
measurements of the same object vary. The more precise a measuring system is, the closer
lie the measured values together.
Figure 2.1 visualizes the definition of accuracy and precision in a mathematical sense.
The distribution of a set of measurements can be expressed in terms of a Gaussian probability
density function. The peak of this distribution corresponds to the mean value of the
measurements. The distance between the mean value and the reference ground truth value
determines the accuracy of this measurement. The standard deviation of the distribution
can be used as measure of precision.
It is important to state that accuracy does not have to imply precision and vice versa.
For example the measuring result of a tube of 50mm length could be 50 ± 20mm. This
statement is very accurate but not very precise. On the other hand a measuring system can
be very precise, but not accurate if it is not calibrated correctly. Thus, good measurements
for industrial inspection tasks have to be both accurate and precise.
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