boundary. Both
D
and
d
should be selected less than a pre-
defined threshold called
T
3
. This threshold directly relates to
the nominal accuracy (
NA
) of the images. Different values of
this threshold are tested experimentally in the next section.
The image and object spaces triangles are assumed
matched if all of their three true lines are found matched via
the abovementioned procedure.
• Accuracy Assessment of a Transformation
: The root
mean square error (
RMSE
) of a proper transformation
model is the last criterion. Here, a pair of two triangles
in image and object spaces (the match-triangles-candi-
date) are assumed matched if their
RMSE
value is lower
than a predefined threshold. This threshold should be
selected based on the geometrical characteristics of the
images and considered equal to
T
3
as discussed in the
previous criterion.
It should be mentioned that the most important
criteria which influence the accuracy and reliability of
the results are these two last factors. So the only key
threshold is
T
3
.
3. Since a line may be fragmented to several segments,
similar results (reasonably, similar parameters of
transformation function) are achieved by the triangles
produced from these fragmented line-segments.
Consequently, after applying the screening-procedure,
the similar triangles are grouped for the sake of more
speeding the next procedures. The grouping, performed
on all the remaining match-triangles-candidates, is
carried out based on the scale factors and rotation
angles of the triangles. These parameters are already
obtained using the solved transformation. The triangles
with similar scale factors and rotation angles are all
grouped. The similarity is checked using a threshold.
In this research, the thresholds of 0.1 degree and 0.01
are selected for rotation angles and scale factors, re-
spectively. Among the match-triangles-candidates of an
identical group, the one with smallest
RMSE
is chosen
as the representative and the other are removed as be-
ing known dependent ones that impose unnecessary
computational efforts.
4. Using the above procedure, only a limited number
of match-triangles-candidates are remaining. As
noted earlier, the matching-phase is aimed to find a
match-triangles-candidate with maximum numbers of
conjugate-lines. Therefore, only the remained match-
triangles-candidates are introduced iteratively to the
next steps to find the correspondence of crossing-lines
(match-lines). To do so, all possible pairs of crossing-
lines (Figure 2) are generated for each remaining
match-triangles-candidates and are regarded as match-
lines-candidates.
5. Here again a screening-procedure is run to investigate
the correspondence of match-lines-candidates. Con-
sidering the input match-triangles-candidate, for each
match-lines-candidate, three inner relative angles as
well as generated-lengths are calculated (Figure 2).
Using these elements, the first and second criteria of
screening-procedure are investigated. Then, for the
remained pairs, the end-points of their true-lines are
transformed to image space. The transformed lines are
used to check the third criterion of screening-proce-
dure (Figure 4). The pairs satisfying these criteria are
allowed to introduce their
MGP
s (three
MGP
s as shown
in Figure 2) for the next computations. For each match-
lines-candidate, at least two out of three
MGP
s should
be satisfying the third criterion.
6. For each match-triangles-candidate, the match-lines-
candidates passed the screening-procedure, are counted.
All the accepted match-triangles-candidates as well as their
accepted match-lines-candidates are introduced to the
decision-procedure.
7. In the decision-procedure, the pair with maximum
number of accepted match-lines-candidates is consid-
ered as the local winner. The accepted lines of the local
winner are also regarded as local matched-lines.
By now, one object-triangle is assigned to each image-triangle
as the qualified match-triangles-candidate. Some image-
triangles may have no qualified match-triangles-candidate.
These local winners in addition to their qualified match-lines-
candidates (called local matched-lines) are introduced to the
final-phase.
The flowchart of the proposed
SLIM
is demonstrated in
Figure 5.
Phase 3: The Procedure of Final-Phase
Among the above local winners, the one with maximum num-
bers of local matched-lines is considered as global winner.
The local matched-lines of the global winner is regarded as
global matched-lines. However, it is possible that more than
one global winner may exist in real datasets (e.g., in datasets
with repetitive patterns). So, the below procedure should be
repeated for all global winners to find the best results.
For each global winner, the correspondence of a limited
number of lines (global matched-lines) can be determined in
matching-phase due to the considered intersection angle. To
increase the amount of matched-lines, the correspondence
of all other inliers is determined based on the first and third
screening criteria as discussed earlier in the final-phase.
After applying the above procedure for all global winners,
the one with maximum number of matched-lines is consid-
ered as the best result. The best global winner in addition to
its all matched-lines are the output of the
SLIM
.
The final output of the
SLIM
could be used to estimate the
coefficients of a parametric or nonparametric transformation
between two spaces as the third step of registration.
Experimental Results and Accuracy Assessments
Dataset Specifications
To evaluate the performance of the proposed
SLIM
as well as
its concepts, this paper used three different datasets. The first
and second ones are a GeoEye, as well as an Ikonos-Geo Im-
age over Uromieh City, North West of Iran and Hamedan City,
West of Iran, respectively. The specifications of these two high
resolution satellite images (
HRSI
s) are listed in Table 1.
Additionally, as the third dataset, a resized Ultracam-D image
over Tehran, capital city of Iran was also used. Its specifications
are listed as Table 2. This image was used to evaluate the reli-
ability of the proposed method in areas with repetitive patterns.
Moreover, three 1:2000 vector maps over the introduced test
fields were also used. The used datasets are shown in Figure 6.
In this paper, the linear features for the first dataset are
extracted manually with a precision about two to three pixels.
Additionally the linear features for the second and third data-
sets are extracted also manually with a precision about one to
two pixels. The lengths of extracted line-segments for satellite
images are larger than 150 pixels and 100 meters in both im-
age and object space, respectively.
Parameter Settings and Experimental Results
In this investigation, the mentioned thresholds for different
parts of the proposed
SLIM
are selected experimentally by
trial and error. Hence, different values of these thresholds are
tested in this subsection.
In the following tests, two evaluation factors are intro-
duced termed validity-factor and capacity-factor. The former
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
May 2016
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