An Iterative Approach to Acquire Linear Features under the constraints of their knowledge in Object Space
the average height of this 3-D linear segment will be simultaneously introduced as the constraints in the second iterative process. Besides the additional height constraint, the second iterative process still uses the core algorithm to match and link the linear segments which are the members of this strongest linear structure. The first and second iterative processing procedure will be applied to the linear segments whose structures are from strongest to weakest.
Subsequently the third iterative process is applied to the remaining linear segments that are the members of the successfully processed linear structure. The same Core Algorithm will be also utilized and height constraint is also considered in this step. This process proceeds repeatedly until the remaining linear segments don't meet the requirement. Finally, Core Algorithm together with height constraint will be employed to those remaining linear segments that locate in the certain range of those already successfully processed linear segments repeatedly until no linear segment meets the above requirements.
Therefore, this iterative approach consists of four steps with one core algorithm and one additional height constraint. The geometric constraint in these four steps becomes less and less and the height constraint is also looser and looser. However, the relevant constraint of object knowledge about 3-D linear segments in Core Algorithm is always unchanged no matter which step it uses.
Fig.3: the diagram of iterative approach
Now
take the Fig.3 as an example. The further
iterative approach will start from the stronger
structure
A which consists of one
junction and three neighboring linear segments
A1,
A2 and
A3. If the process succeeds, then
A1,
A2, and
A3 will be processed at once. In
this case, linear segments
A2 is
also the neighboring linear segment of the weaker
structure
B. It is assumed that
the process didn't succeed in handling linear
segment
B due to fail in finding
the corresponding junction in right image. The
iterative process will process it again in the
third step because linear segment
B
is the adjacent linear segment of linear
segment
A2, which has been
successfully processed. Next, linear segment C is
close enough to successfully processed linear
segment
A1, the process will be
initialized again. If the linear segment
C
also is successfully handled, then the
linear segment
D
is also processed again due to the same reason. Otherwise, all the process will stop.
Apparently if only the first
iterative processing is applied, it might be
impossible to obtain the results from linear
segment
B,
C,
and
D
. Because the result is feedback to restrict and guide another process once more to handling others, therefore, it is possible to produce more results. From the above discussion, the iterative approach does increase the amount of successfully matching and linking the linear segments. Next section will give some experiments.
4.Experiments and Results
This section will describe the results of the experiments. The pixel resolution of image pair is 30µm; image scale is about 1:8,000; and their image size is 180*180 and 180*225, respectively.
The associated thresholds for Core Algorithm in object space are described as follows:
The reasonable horizontal distance of 3-D edge piece (dP(i)) is set as 0.12m. Beside the threshold for the absolute value of average change rate of height is chosen as 1 m/m, the relevant thresholds are set as:
In the initial screening of possible candidates, 10 degrees for the azimuth difference threshold and 20 gray values for the difference of mean gray values of the flanking mate. Plus, 8 for the number of reliable 3-D edge pieces and 3m/m for the standard deviation of average change rate of height.
In subsequent matching and linking process, 5 for the number of reliable 3-D edge pieces.0.2 m/m for the difference of average change rate of height between candidates and the initial linked linear segment.
Fig.4: The result of matching and linking in object space according to their geometric priority
Fig.5: The result of matching and linking in object space via further iterative process: height difference 0.5 m
The result in Fig.4 is acquired only by the first processing procedure of iterative approach. Only 7 linear segments are successfully acquired. Some line segments could not be successfully processed because the geometrical structure can't meet the requirement of initial screening. However, after the concept of iterative approach is used, the results in Fig.5 show that 11 line segments are acquired. Additional 6 linear segments are obtained. The height difference in third and fourth process is set as 0.5m in the test of Fig.5. If the constraint of height difference is relaxing to 5m, two more will be successfully acquired, not shown here due to short space. Therefore, it could say that the concept of iterative approach could be helpful to get more 3-D linear segments. The results prove this concept could be applicable. Only one correspondence seems questionable, indicated by linear segment a at the upper left in Fig.5. This case is often happened in the urban images of Taiwan area due to the structures themselves.
5.Conclusions
From the experiment, this iterative approach does increase the number of matched and linked line segments for the next task. Nevertheless the simple weighting criterion is worthwhile to further investigation. Anyway, the increasing amount will be helpful for the subsequent relevant tasks.
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