=Paper=
{{Paper
|id=Vol-2391/paper31
|storemode=property
|title=Optimal tuning of the contour analysis method to recognize aircraft on remote sensing imagery
|pdfUrl=https://ceur-ws.org/Vol-2391/paper31.pdf
|volume=Vol-2391
|authors=Evgenii Dremov,Sergey Miroshnichenko,Vitalii Titov
}}
==Optimal tuning of the contour analysis method to recognize aircraft on remote sensing imagery ==
https://ceur-ws.org/Vol-2391/paper31.pdf
Optimal tuning of the contour analysis method to recognize
aircraft on remote sensing imagery
E N Dremov1, S Yu Miroshnichenko1 and V S Titov1
1
South-West State University, 50 Let Oktyabrya street, 94, Kursk, Russia, 305040
e-mail: evgeni-dremov@yandex.ru, oldguy7@rambler.ru, titov-kstu@rambler.ru
Abstract. In this paper, we describe the experimental results of aircraft recognition on optical
remote sensing imagery using the theory of contour analysis. We propose the a method to
calculate optimal values of the contour’s items quantity and the classification threshold through
measuring within- and between-class distances for all possible training set instances
combinations with followed by detection and minimization of the type I and II errors. We
discuss the construction of contours’ similarity measures combining the principles of finding
the most appropriate reference instance and calculating the average value for the whole class. It
is shown that the proposed parameters' tuning method and the similarity function make contour
analysis capable to train on compact non-uniform datasets and to recognize aircraft on the
noisy and less detailed images.
1. Introduction
The mathematical apparatus of contour analysis is an effective approach to solve the problem of
objects recognition using their shapes as the distinctive features [1,2].
To reach affine transformation invariance researchers in the field of aircraft recognition use a
combination of few features and methods such as contours, Zernike moments and wavelet coefficients
in [3], Radon transform, PCA and kNN classification in [4], HOG, graph theory and an object
reconstruction in [5].
In contrast, contour analysis uses the single similarity measure of two vector-contours, the module
of the normalized dot product (NDP) that is invariant (insensitive) to transfer, rotation, and
proportional scaling of the recognized object towards the reference one. The similar recognition
methods produce a unique value per each classes pair [6-8] and require an additional clustering
procedure to match an object to a certain class. In contrast, the NDP module provides a uniform
similarity measure of two contours within the range [0..1] where 1 – denotes the identical instances.
Moreover, the NDP itself is a complex-valued number describing contour’s scale and rotation angle
relatively the reference instance.
Despite the listed above advantages, the NDP has its own limitations, which include the need to
select the values of the vector-contour’s items quantity and the classification threshold used to decide
whether the corresponding object belongs to a certain class.
The first limitation is a consequence of the fact that in order to calculate the NDP value, the
compared contours should have the same items' quantity (however, the length of the vector-contours -
the sum of its vectors lengths - does not have to be equal). The problem of optimal vector-contour’s
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items quantity selection is to find a balance between the lower values, smoothing together little-
informative details and distinctive features of the recognized object, and higher values, providing more
distinctive features but making the instances the single class more unlike [6].
The second limitation arises from the of the classification rule used to decide whether a given
vector-contour belongs to one of the classes and consists in the need to select a threshold value
corresponding to the minimal similarity value between the reference objects. This value for each class
is determined by the differences between the instances in the training dataset.
Comparing to the state-of-the-art convolutional neural networks (CNN) [9, 10], requiring hundreds
of images to train, contour analysis’s based recognition methods are capable of dealing with compact
and nonuniform datasets containing less than 10 instances per class. Moreover, CNNs require transfer
learning techniques [11] to operate on images with spectral parameters different from the training ones
(for example, created by the sensor of another type). To the contour analysis list of disadvantages, we
should write a much shorter range of applications, as the recognition process is driven by the only
feature – the object’s shape, together with the strong addiction to the segmentation method’s quality
used to extract the object from an underlying surface [12-15].
This article considers the application of the mathematical apparatus of contour analysis to
recognize the aircraft’s class on remote sensing imagery. The shape of the aircraft on view from above
is the primary distinctive feature determining its class. However, aircraft instances of the same class
can have differences in shape due to the following reasons: the presence or absence of the external
wing-mounted armament or equipment, the disassembly of aerodynamic surfaces (slats, flaps,
rudders), engines and rotary blades, wings with variable geometry, folded wings for naval aircraft.
Shape variations can also be caused by the segmentation algorithms that incorrectly react to the
boundaries of its illuminated and shaded areas, as well as closely located airfield equipment.
The article has the following structure. Section 2 contains a formal statement of the recognition
problem used to determine the list of optimized parameters. Section 3 is devoted to the description of
the features of the training and test datasets: the first one serves as a data source to calculate optimal
values of the parameters, the second one – to verify results. Section 4 shows the process and the results
of the experiment to obtain the value of the classification threshold for each class in training dataset.
Section 5 is devoted to the results of the experiment to determine the values of the vector-contour’s
items quantity required to calculate the NDP value for each class. Section 6 describes the selection of
similarity value calculation criterion and the experimental results of the tuned contour analysis
method. Section 7 contains a discussion and suggestions for future work.
2. Formalization of the recognition problem
We introduce the following notation:
C {Ci }1NC – is a set of aircraft classes, where Ci – is an aircraft class with index i , N C – is the
number of aircraft classes.
Γi ik }kNi1 – is a set of reference vector-contours (hereinafter referred to as “references”) of i-th
class, k – is an reference instance index, N i – is the number of instances in the i-th class, ik –
instance contour of i-th aircraft class with index k.
Each instance described by a vector-contour ik , consisting of l complex-valued elements called
elementary vectors ik , designated as:
ik ( ik (1), ik (2),..., ik (l )) .
The mathematical apparatus of contour analysis is applicable only to contours with the equal items
quantity. In practice, images contain objects that have contours with an arbitrary number of elements.
The process to transform the vector-contour to have strictly l elements is called “equalizing” [2]:
Гik fe
Гik (l ), Гik (l ) { ik (n)}1l (1)
.
The NDP is calculated by the formula:
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(l ), (l ) , (l ), (l ) ( (n), (n)) ,
l
(ik , jm , l )
ik jm
(2)
| (l ) | | (l ) |
ik jm ik jm
ik jm n 1
where ik (l ) and jm (l ) – are equalized vector-contours, ik (l ), jm (l ) – is a vector-contours dot
product, | ik (l ) | and | jm (l ) | - the norms (lengths) of the corresponding vector-contours.
The operations (2) and (3) with vector-contours are both performed on vectors of complex-valued
numbers, which allows achieving the following features [1,3]:
1. The sum of the elementary vectors of a closed contour is zero.
2. Invariance to the transfer (Figure 1): the vector contour does not depend on the parallel transfer
within the original image.
3. Invariance to the rotation (Figure 1): rotating an image by a certain angle is equivalent to rotating
each elementary vector by multiplying it by a complex factor.
4. Invariance to scaling (Figure 1): changing the image size is equivalent to multiplying each
elementary vector by the real scale factor.
5. Changing the starting point leads to a cyclic shift of the vector contour. The NDP is not invariant
to the change of the initial point.
The later feature requires to transform the NDP to the cross-correlation function (CCF) of vector-
contours, which in addition to the invariance properties of (2) is insensitive to the initial point’s shift:
(i, j, k , m, l ) max
ik (l ), (jms ) (l ) , (3)
s | ik (l ) || jm (l ) |
where s 0,..., l 1 is a shift from to the initial point, (jms ) (l ) – is a contour obtained from jm (l ) by
the cycle shift of its elementary vectors to s-elements.
Figure 1. NDP invariance to the transfer, rotation, proportional scaling.
The classification rule to determine the affiliation of a certain contour Г to Ci class is:
C : i arg max( f (, Γ ) T ) ,
i i i
i i
,
C ( ) (4)
: i max f (, Γi ) Ti ,
i
where Ti – is the classification threshold value for the aircraft of the i-th class, f (, i ) [0,1] – is the
function for calculation the similarity value of the given vector-contour to the set Γ i of reference
objects.
The function for similarity value calculation can apply one of the two following criteria:
1. Maximum CCF for a vector-contour Г and one of the reference instances ik :
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f (, Γ ) max
(l ), (l ) ,
i
(s)
ik i
(5)
| (li ) || ik (li ) |
1 i
k ,s
where li - is the optimal value of the vector-contour's items quantity for i-th aircraft class.
2. The mean CCF value for a i-th whole class:
1 Ni (li ), ik( s ) (li ) .
f 2 (, Γi ) max
Ni k 1 s | (li ) || ik (li ) |
(6)
The aim of the article is to create a contour analysis tuning method by the solution of the following
problems:
1. Determine the optimal values of the vector-contour's items’ quantity L {li }iNC1 and the
classification threshold T {Ti }iNC1 in terms of the minimum total number of I and II type errors.
2. Select a criterion to calculate the similarity value of the vector-contour to a set of reference
instances Γ i .
3. Dataset details
The dataset we used within the experiment is divided into the training part, used to tune the
recognition method’s parameters and the test part for the verification.
The training dataset contains aerial images of optical range with a resolution of 0.15 m / pixel
displaying the parking of decommissioned and reserved aircraft at the Davis-Monthan airfield [16].
The training dataset is compact and includes 430 images of the aircraft of eight classes: B-1, B-52, C-
5, C-37, C-130, C-135, P-3, and S-3.
Figure 2 shows the examples of all 8 aircraft classes of the training dataset. Table 1 lists the
characteristics of the classes and the instances’ contours.
B-1 B-52 C-5 C-37
C-130 C-135 S-3 P-3
Figure 2. Image examples of aircraft in the training dataset.
The classes of the training dataset differ significantly from each other both in the number of
instances and in the degree of within-class similarity of their contours. An example of a significant
difference in the instances is shown in Figure 3 for B-1 class: the nose cone (Figure 3a), the engines
(Figure 3b), the slats, flaps, landing shields, rudders, stabilizers (Figure 3c, d) were removed. The
other classes (for instance, B-52) have minimal differences in instances.
The described differences in the training dataset require to calculate the optimal values of vector-
contours' items quantity and the classification threshold individually for each class.
The test dataset is equivalent to the training one and contains 421 aerial images of three resolution
levels: 0.15 (10 images), 0.3 (10 images) and 0.5 meters per pixel (402 images), shot in the Davis-
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Monthan and a few operating airfields. Figure 4 shows the examples of the aircraft included in the test
dataset (the details of the test dataset are given in Table 2).
Table 1. Characteristics of contours in the training dataset.
Aircraft class B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3
Instances count 17 10 20 11 135 81 92 64
Mean items’
1132 1945 2404 1227 1570 1420 1458 1132
quantity
Items’ quantity
histogram
a) b) c) d)
Figure 3. Instances of B-1 aircraft having various dismantled elements.
B-1 B-52 C-5 C-37
C-130 C-135 S-3 P-3
Figure 4. Images examples of the aircraft in the test dataset.
Test images of 0.3 and 0.5 meters per pixel (for instance, B-1 and C-130 on Figure 4) have
significant visual differences from the training set in contrast and brightness as well as in
lighting/shading scheme so the major remaining recognition feature is the shape. Test images of 0.15
meters per pixel were shot on the other season, have greater camera-to-surface angle, differences in
color rendition and contain much more noise that seems to be caused by the lossy compression. All the
described features of the test dataset strongly affect aircraft contours challenging the robustness of the
proposed contour analysis’s parameters tuning method.
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Table 2. Characteristics of contours in the test dataset.
Aircraft class B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3
Instances count 7 6 48 11 57 102 142 49
Mean items’
1263 1884 2441 1177 1483 1315 1345 1084
quantity
Items’ quantity
histogram
4. Optimal classification thresholds calculation
To calculate the optimal classification thresholds T {Ti }iNC1 , the measurements of within-class and
between-class distances were made for all possible combinations of training dataset instances.
The measurement of the within-class distance is a calculation of the CCF (3) for a particular non-
coincident pair of vector-contours of the same class. The measurement of a between-class distance is a
calculation of CCF for a particular pair of vector-contours of different classes.
An error of a within-class distance measuring (type II error or a false negative measure) [17] is the
value of within-class distance that is less than the specified value of the classification threshold T:
1, (i, i, k , m, l ) T
ei (k , m, l , T ) . (7)
0, (i, i, k , m, l ) T
The error in between-class distance measuring (type I error or a false positive measure) [17] is the
value of the between-class distance which is greater than the specified value T:
1, (i, j, k , m, l ) T
eij (k , m, l , T ) . (8)
0, (i, j, k , m, l ) T
It is clear from formulas (7) and (8) that an increase in the threshold value T reduces in the number
of type I errors but concurrently increases in the number of type II errors and vice versa.
The optimal value for each aircraft class corresponds to the minimum number of type I and II
errors for the given range of the vector-contour elements quantity l.
The relative type II measurement error (the ratio of the within-class distance measurement errors to
their total number) for the i-th class with the given l and T is defined as:
N (i, l , T )
EIC (i, l , T ) IC , (9)
Ni ( Ni 1)
Ni Ni
IC (i, l , T ) e (k , m, l,T ) ,
i (10)
k 1 m 1, m k
where IC – is the number of type II measurement errors.
The relative type I measurement error (the ratio of the between-class distance measurement errors
to their total number) is calculated with the formula:
N (i, l , T )
EBC (i, l , T ) BC NC , (11)
Ni N j
j 1, j i
NC Ni Nj
N BC (i, l , T ) eij (k , m, l , T ) , (12)
j 1, j i k 1 m 1
where N BC – is the number of type I measurement errors.
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At each classification threshold value, the total relative measurement error Emin () is calculated as a
minimal sum of relative type I and II measurement errors and represents an objective function [18] to
compute an optimal threshold value T for Сi class:
Emin (i, T ) min EIC (i, l ,T ) EBC (i, l ,T ) . (13)
l
The vector-contour elements quantity l varies within the interval l 100,...1000 with a step of 10.
The interval boundaries are explained by the fact that the distinguishing features of the most aircraft in
the training dataset are lost at l 100 , and l 1000 reaches the minimum quantity of items for some
reference instances.
The classification threshold changes within the interval T 60,...,80 with a step of 1. The
interval is chosen according to the following arguments: at T 60% many instances of different
classes are similar to each other, whereas at T 80% a within-class similarity becomes insufficient
due to the variety of contour shapes within a single class.
The experimental data was used to create graphs of the total relative measurement error (13)
dependence from the classification threshold for each aircraft class. The graphs shown in Figure 5
provide the characteristic features of the most interesting classes of the training dataset. The B-1 class
is described by significant differences between its instances, which is confirmed by high values of (13)
in the range of 6-12% for the entire graph in Figure 5a with a slight predominance of type II
measurement error. The B-52 class graph, on the contrary, demonstrates a rapid decline in type I error
at a threshold of 60-70% with the following near-zero type II error on the right side of the graph.
As for the C-130 and P-3 classes of propeller aircraft (Figure 5b), the outwardly similar contours
are characterized by close graphs of (13) with the predominance of type I error for C-130 and type II
error for P-3.
a) b)
Figure 5. Total relative measurement error (13) dependence from the classification threshold for
classes B-1 / B-52 (a) and C-130 / P-3 (b).
Formula (13) was used to calculate the optimal classification thresholds T {Ti }iNC1 for each class in
the training dataset (the results of the calculation are given in Table 3):
Ti arg min( Emin (i, T )) . (14)
T
Table 3. Optimal classification thresholds.
Class index 1 2 3 4 5 6 7 8
Class name B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3
Optimal value Ti , % 63 71 66 69 69 69 66 74
5. Optimal vector-contour’s items quantity calculation
The optimal values of vector-contour’s items L {li }iNC1 for each aircraft class are calculated on the
basis of the total relative measurement error using the previously determined threshold T {Ti }iNC1 .
The sum of the relative measurement errors of type I (9) and II (11) errors represents an objective
function to compute an optimal value of the items’ quantity li for Сi class:
E(i, l ) EIC (i, l , Ti ) EBC (i, l , Ti ) . (15)
Graphs (Figures 6-7) show the vector-contour’s items optimal quantity corresponding to the
minimum of (15) marked with a vertical line. The optimal items quantity for B-1 class (Figure 6a) lies
near the intersection of the types I and II error graphs. The errors for a given class vary widely due to
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the significant differences in its instances. The B-52 class items optimal quantity (Figure 6b) is
determined only by the minimum of type I errors.
a) b)
Figure 6. Total relative measurement error (15) dependence from the B-1 (a) and B-52 (b) vector-
contour's items quantity.
The optimal value of C-130 (Figure 7a) and P-3 (Figure 7b) classes biased towards type II error
and is to the right of the intersection of both error graphs. Class C-130 is characterized by a higher
total error value compared to P-3 due to more significant differences between the references instances
of this class.
a) b)
Figure 7. Total relative measurement error (15) dependence from the C-130 (a) and P-3 (b) vector-
contour's items quantity.
Formula (15) was used to determine the optimal values of vector-contour's items quantity
L {li }iNC1 for each class in the training dataset (the results are presented in Table 4):
li arg min( E (i, l )) . (16)
l
Table 4. Optimal values of the vector-contour’s items quantity.
Class index 1 2 3 4 5 6 7 8
Class name B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3
Optimal value li 640 910 900 910 810 680 650 580
The proposed optimal items’ quantity calculation method was experimentally compared to the most
widely used heuristic methods including the use of:
(a) the minimal items’ quantity of the certain class’s instances to minimize the type II error;
(b) the maximal items’ quantity of the certain class’s instances to minimize the type I error;
(c) the recognized object’s items quantity to retain its actual level of details.
The table 5 represents the total relative measurement error (15) per each aircraft class along with
the mean value for all the heuristic methods and the proposed one.
Table 5. The total relative error for the proposed method and for heuristics.
Row name Total relative error (15), %
Class index 1 2 3 4 5 6 7 8 Mean error
through all
Class name B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3
classes
Heuristic (a) 12.18 20.00 38.66 0.09 13.68 7.59 11.97 8.38 14.07
Heuristic (b) 12.18 13.33 26.29 0.09 21.23 3.70 10.00 3.97 11.35
Heuristic (c) 11.49 8.89 19.29 0.15 11.42 2.53 7.32 2.58 7.96
Proposed
9.42 0.00 2.13 0.00 6.51 0.23 4.18 0.76 2.90
method
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The differences in results of heuristic methods (a-c) for certain classes emphasize the training
dataset’s irregularity. The best heuristic solution is to use items' quantity of the recognized object,
however, the proposed tuning method provides around 3 times less total measurement error.
6. Criterion for similarity value calculation
To estimate the developed parameters tuning method and to select a criterion for the similarity value
calculation of a recognized vector-contour Г to a set of reference instances Γ i , we used the test dataset
described in section 2. The test images of 0.3/0.5 meters per pixel resolution are upscaled to 0.15
hence the instances of a certain class have close items’ quantities through the whole dataset.
The recognition results for the test datasets obtained by the classification rule (4) in combination
with the functions for similarity value calculation f1 (5) and f 2 (6) are presented in Table 6.
Table 6. The results of test datasets recognition with the classification rule (4) in combination with
functions f1 and f 2 .
Class index 1 2 3 4 5 6 7 8
Total
Class name B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3
Type I errors 0 0 3 0 3 0 1 0 7 (1.66%)
f1 Type II errors 1 0 0 0 0 0 0 0 1 (0.24%)
Total errors 1 0 3 0 3 0 1 0 8 (1.9%)
Type I errors 1 0 2 0 0 29 0 0 32 (7.6%)
f2 Type II errors 5 5 6 11 45 39 31 1 143 (33.9%)
Total errors 6 5 8 11 45 68 31 1 175 (41.5%)
Function (5) performs much better than (6) that is explained by the fact our parameters tuning
method uses a similar to (5) pair-wise within-class and between-class distance calculation rule to
define type I and II measurement errors.
To reduce errors number we modified the classification rule (4) to combine the functions (5) and
(6), integrate their merits and mutually compensate shortcomings. The modified classification rule
becomes the following:
C : i arg max( f (, Γ ) T ) ,
i i i
2 i i
C () Ci : i arg max( f1 (, Γi ) Ti ) , i max f 2 (, Γi ) Ti , (17)
i i
i
: i max f1 (, Γi ) Ti ,
i
The results of the test datasets recognition with the modified classification rule (17) are presented
in Table 7.
Table 7. Test dataset recognition results with modified classification rule (17).
Class index 1 2 3 4 5 6 7 8
Total
Class name B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3
Type I errors 0 0 1 0 0 0 0 0 1 (0.24%)
f1 + f 2 Type II errors 1 0 0 0 0 0 0 0 1 (0.24%)
Total errors 1 0 1 0 0 0 0 0 2 (0.48%)
The remaining type II error for the contour analysis method belongs to class B-1 and indicates the
need to expand its training dataset with instances of the operating (non-disassembled) aircraft. The
type I error for C-5 is explained by the segmentation algorithm fault.
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7. Conclusion and discussion
In this paper, we presented the results of the experiment aimed to tune the contour analysis method to
recognize aircraft on aerial imagery. We calculated optimal values of the vector-contour’s items
quantity and the classification threshold through measuring within- and between-class distances for all
possible training set instances combinations with the following detecting and minimization of type I
and II errors. It is shown that each class has its own optimal values of these parameters due to the
features of the reference instances of the training dataset. We proposed a classification rule that
combines the merits of functions based on the best instance match and the mean CCF for class
respectively.
The vectors of further research are the development of new segmentation methods that allow
solving the aircraft edges detection problem upon the conditions of camouflage, poor contrast with the
underlying surface, illuminated and shaded areas, as well as close-lying airfield equipment.
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Acknowledgments
The authors gratefully acknowledge support by CodLix LLC.
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