Geoscience Reference
In-Depth Information
kept and the number of points which have to be eliminated are calculated
based on an initial scale and based on the reduced scale, again using
Töpfer's radical law using equation (5).
In the next step of our algorithm the polarization-centre (
P
c
) which has the
maximum average length to all other points will be calculated using equa-
tion (1). Then all azimuth angles from the polar centre
P
c
to each point will
be calculated using equation (3). Subsequently the results are sorted in a
Matrix
sort_angle(distances, azimuth angles)
according to the increasing
azimuth direction angle values. Duplicates in the Matrix will be elimi-
nated.
After that the spectrum line can be displayed in the polarization space (like
in
Figure 1
). In case of 3D-coordnates there are three polarization spaces
of each perspective (xy, xz, yz). Now our new segmentation-process for
defining the spectrum line segments will be done:
•
First the value-differences between all sorted azimuth angles are calcu-
lated. This happens by subtraction of sorted azimuth angle (i) with
sorted azimuth angle (i+1).
Formula (3):
Matrix
{
|
d
_
sort
_
angle
=
|
sort
_
angle
(
)
−
sort
_
angle
(
+
1
for all i = 1..n-2 whereas n = number of all points
•
Now the spectrum line will be segmented in an iterative process. The
spectrum line will be segmented starting with the largest value of the
sorted azimuth angle
max(d_sort_angle)
for the threshold Δα, in other
words the largest difference between two neighbor points in the spec-
trum line. Based on that segmentation all points that follow Qian's
requirements for preserving characteristic nodes - like described in the
previous chapter - will be kept, all others eliminated. To be more pre-
cise if the azimuth angle difference between two neighboring points of
the spectrum line is larger than Δα then set a threshold.
Formula (4):
if
Δα
< [|
sort_angle
(
i
)
-
sort_angle
(
i
+1
)|
]
then set a threshold
•
In the iteration that step will be repeated until the number of kept points
are equal to (or not more than) the user-defined (in case of a user-
