by the control points. This requirement is important for
obtaining a high precision of transformation.
The picture has to be taken so that the whole rope (the lower
catch and the upper catch) is visible in it. Otherwise the catches
could not be used as control points.
Experience shows that, in order to get reliable results, at least
60 % of the rope’s length should be available for measurement.
The automating and computing process begins with taking
picture(s) (at least one) of the rope with a digital camera.
Pictures are then transmitted on site from the camera to the
computer. When in the computer, the pictures can be screened
by an elaborated system and all processing activities, such as
control points measurement, rough rope's position
determination, running the line following algorithm, and,
finally, computation of the horizontal tension strength
component of the rope, are carried out. A human operator
determines control points and rough rope's positions manually -
further steps are automated. When control points are measured
and the position of the rope is marked, the line following
algorithm is activated. When the work of the line following
algorithm has been completed, the results are displayed on
screen as green points marked on the rope. When the human
operator evaluates the results, he/she can decide whether to
repeat the line following analysis or to proceed to the next step,
ie. the computation of the horizontal tension strength
component of the rope.
When the final horizontal tension strength component of the
rope is determined, the decision concerning applying proper
correction to the rope's tension and repeating the entire process
is made.
The computation of the horizontal tension strength
component of the rope consists of two steps. The first one is the
computation of catenary parameters (equation 1, figure 1) in the
iteration process of the Least Square Method. Usually, a large
number of points is gained after finishing the work of the line
following algorithm- in the example tested, there were about
1600 points. The iteration process did not last too long — usually
after three iterations sufficient accuracy was obtained. With the
catenary parameter k, the calculation of the horizontal tension
strength component of the rope becomes very simple and
functions according to equation 2.
3. LINE FOLLOWING ALGHORITHM
Before line following algorithms were elaborated, a
thorough analysis of rope images had to be carried out.
The rope image can be considered as being shaped as a longish
hump or ditch, depending on whether the image is negative or
positive. An example of a rope’s image, approximated by a
kriging interpolation is shown in figure 3.
The image of the line can be modelled by a mathematic
function. Such an introduced model was based on [3]. Here I
only notice two conditions that should be fulfilled by a curve
received by the slicing image of the rope (along a row or
column) with a vertical plane:
e Possesses a continuous first and second derivative,
* Possesses one maximum and two inflection points.
A model of such a function is shown in figure 4a.
The task of the line following algorithm is the semi-automatic
determination of a set of points along a ridge of a hump
(maximum of the function). The result scores in numerous
(thousands) semi-automatically measured points.
The procedure runs/occurs in following steps:
International Archives of the Photogrammetry, Remote Sensing and Spatial-Information Sciences, Vol XXXV, Part BS. Istanbul 2004
e A human operator places three points to show an
approximate shape of the rope curve,
* The line following algorithm is activated and
automatic measurement is carried out.
Figure 3: An axonometric view of a digital image of a rope. The
pixels are units of horizontal coordinates and their grey level
are the units of vertical coordinates. The original function of the
image was interpolated by the kriging. —
a) EDT =
b)
1.3 5.7 8 11 13 15.17 19
c)
25 27.29 31 33 35 37 39
Figure 4: a) Function of the rope image, b) first derivative, c)
second derivative.
Points which define the rope should be placed along the whole
length of the rope, the first one close to the upper catch, the
second in the middle, the third close to the lower catch. The line
following algorithm starts from the first point and stops on the
third. The analysed segment of the rope should be as long as
possible in order to minimise the number of errors in the results
and assure their reliability (paragraph 2.2).
While the line following algorithm is working, the first step is
to fit the catenary into the three above-mentioned points. This
procedure runs in two courses. In the first course, inflection
points are identified with pixel resolution.
After the first course is finished, the average positions of left
and right edges of the rope are determined. These are to be
used in the filtering process at the end of the procedure. In the
second course, sub-pixel positions of the centres of rope (as the
average of positions of inflection points) are calculated at every
interval and the filtering of erroneous points is carried out.
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