Master Thesis - Hochschule Bonn-Rhein-Sieg

5. Algorithms Master Thesis Björn Ostermann page 66 of 126
As described in chapter 4.3.4 the base of the robot is part of the background data and a virtual base
needs to be added to the detected intrusions. Afterwards a region growing algorithm can create objects
from connected pixels that show intrusions. From those regions the intrusions created by the robot can
be identified with the help of the virtual robot base.
5.2.1 Acquiring the background data
As described in chapter 4.3.2 the data delivered by the camera have a certain error margin. The less
the error in the background data, the better the detection of dynamic objects can be performed. The
background data needs only to be taken once during the set-up phase. Thus to achieve a set of reliable
data, the acquisition of the background is performed by taking several images of the unoccupied
working space. Taking the median distance value in each pixel of those images, using the Kalman
filter [36], reduces the error margin in the data. Tests showed that some surfaces like metal tend to
produce larger errors, which would need a huge amount of data to compensate. Since most of the
surfaces in the workplace of this project are flat, the remaining noise can be reduced by smoothing the
data by applying a small Gaussian blur filter [62]. This filter reduces peaks in the background and also
the amount of necessary sample data is reduced by this measure.
Each combination of pixel position, distance and surface leads to a specific error margin. To estimate
the maximum error in each pixel, used in later algorithms, the smallest value of each pixel is tracked
and recorded, in addition to the median background value.
Due to the similarities in the requirement on the background data, the acquisition of the background
was developed in collaboration with another master thesis [81].
5.2.1.1 Kalman Filter
The Kalman filter [36] was chosen, because of its ability to work on consecutive values with taking
their possible error into account. Its application, as described in this chapter, is commonly known in
data processing. This property of the algorithm allows the processing of unlimited images without the
need for a large amount of memory. In the course of this work it was sufficient to use a set of 500
images during background acquisition.
This filter works in iterations. In the first iteration the filter is set to the currently measured value and
its estimated error. In each of the following iteration the filter uses its previous results and the
currently measured value and estimated error to create a new result.
The estimated error results from the manufacturer information, which is specified to be 1% of the
measured distance (see chapter 3.2).
To compute the currently estimated result x (see Equation 6) and its error � x (see Equation 7), using
the Kalman filter, only the current sensor value z 2 , its error � z and the previous estimation z 2
1 and
its error
� z are needed.
1