IEEE - Aerospace and Electronic Systems - July 2022 - 37

Fahimi et al.
Figure 6.
(a) Original image segment containing the window portal. (b) Laplacian edge detector output. (c) Horizontal and vertical projections of the edge
image. The peaks ofthese projections are to be used for segmenting the image. (d) Segmented image: detected peaks can forma grid ofsegments. It
is clear that the image is oversegmented but this will not affect the optimization process. (e) B image distinguishing darkest segment from others.
(f) Ideal segmentation.
formed in which every pixel that belongs to s is equal to 1,
and otherwise, it is equal to 0, as visualized in Figure 6(e)
Bði; jÞ¼
mulated as follows:
min
t
min
t
CðtÞ
s.t. 0 t 1:0
in which CðtÞ is the cost function defined as
CðtÞ¼
P
(5)
i;j jBði; j; tÞ Bði; jÞj
AðBÞ
CðtÞ
s.t. t 2 Q:
(7)
1;
0;
if ði; jÞ2 s
otherwise.
(4)
The optimization problem of finding the best t is forFINAL
DARK AREA EXTRACTION ALGORITHM
Although the global optimization is capable of finding
optimum t, combining the two aforementioned methods
in a selective search scheme would offer a more computationally
efficient implementation. Thus, we reformulate
the optimization problem as follows:
(6)
where AðBÞ represents the white area of the binary image
(i.e., summation ofB). The numerator in (6) is the absolute
difference between BðtÞ [see Figure 3(b)] and B. By minimizing
it, we seek a t that forces BðtÞ to only reveal darkest
segments of the image and nothing else. However, there are
many situations that Bðt ¼ 0Þ, i.e., an emptyB, has the minimum
distance to B. To avoid this, the denominator in (6) is
considered. Minimizing the proposed cost function guarantees
that a proper t is found such that the binary image B
only detects the dark area inside the darkest segment s.
It could be possible that, we detect the darkest segment of
the image (s) per frame, then we guide the vehicle toward
that segment. The fact is that the whole process offinding s is
rather time-consuming. Moreover, it does not reveal more
than a rectangular approximation of the entrance section. On
the other hand, solving the proposed optimization problem to
find an optimum t; and then applying aforementioned
dynamic thresholding technique is much faster and could be
done framewise. Also, the binary image created by thresholding
could contain exact boundaries of the portal section and
will be used to establish a 6-DoF position estimation whose
merits will be discussed in the " Guidance " section. Derivation
ofthe optimum threshold value is better illustrated in Figure 7.
JULY 2022
Figure 7.
(a) Cost function for all threshold values is plotted as the blue
curve. It is clear that for an appropriate value as a threshold, the
window portal section is detected as a solid and well separated
section. (b) Plot ofthe cost function for a different window image,
which shows the threshold at the minimum cost value is a good
choice for creating the binary image.
IEEE A&E SYSTEMS MAGAZINE
37
IEEE - Aerospace and Electronic Systems - July 2022

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