=Paper=
{{Paper
|id=Vol-2534/37_short_paper
|storemode=property
|title=Combination of Neural Network and Linear Filtration for Objects Detection
|pdfUrl=https://ceur-ws.org/Vol-2534/37_short_paper.pdf
|volume=Vol-2534
|authors=Adilbek K. Shakenov
}}
==Combination of Neural Network and Linear Filtration for Objects Detection==
https://ceur-ws.org/Vol-2534/37_short_paper.pdf
Combination of Neural Network and Linear Filtration
for Objects Detection
Adilbek K. Shakenov
Institute of Automation and Electrometry, Novosibirsk, Russia, adil.shakenov@ngs.ru
Abstract Several approaches to the use of neural networks for the detection of objects on
spatially inhomogeneous backgrounds are considered. Implemented a method for
constructing a classifier for detecting objects directly from the observed fragments. An
approach is proposed, which consists in a combination of the method of optimal linear
filtering and convolutional neural networks. It is shown that the applied approach allows
reducing the probability of a false alarm while maintaining the probability of detecting an
object.
Keywords: object detection and recognition, convolutional neural networks, machine
learning, small-sized objects
1 Introduction
The problem of detecting small-sized, low-contrast objects has been actively studied for the past decades [1].
Research in this area remains relevant, as evidenced by the large number of works on this topic published in
subsequent years. When small-sized, low-contrast objects are detected, their shape and size correspond to the
hardware function of the system and do not contain enough information for reliable detection. An important feature of
the detection algorithms for such cases is the need to evaluate and exclude the underlying background from
consideration. The most effective approach for this is the spatio-temporal filtering of image sequences [2]. However,
in some cases, due to the peculiarities of the geometry of the survey or the computational limitations of the data
processing system, it is necessary to evaluate and suppress the background from one image. There is a known
approach to solving the problem under consideration, which makes it possible to obtain an optimal linear filter for the
case of a stationary background with a known covariance matrix [3]. Various algorithms for estimating and filtering
the background according to the observed local neighborhood are actively developed and applied, for example,
bilateral [4], median [5] filtration, optimal linear prediction [6,7], and other heuristic methods [8-11]. The optimal
linear filtering method was developed under the assumption that the statistical properties of the background are the
same throughout the frame field. This assumption may not hold for a wide range of observed backgrounds. This
determines the relevance of the search for new approaches to solving the problem of detecting small-sized, low-
contrast objects on spatially inhomogeneous backgrounds.
Recently, methods of recognition and detection of learning neural networks have been actively developed
[12]. Examples of use in small objects can be found in [13-16]. In neural networks, a fairly large number of
intermediate features are used in the process of processing fragments, so it can be expected that their use will improve
the results of linear filtering precisely on spatially heterogeneous backgrounds. In addition, the ability to train the
network directly from the observed data makes it possible to easily adapt this approach to a large number of
background and observed objects
2 Problem Statement
It is necessary to develop an algorithm for detecting objects on heterogeneous backgrounds, which improves
detection characteristics compared to the optimal linear filtering algorithm using trained neural networks.
Copyright ยฉ 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0
International (CC BY 4.0).
3 Detection of objects with training in observable fragments
One of the ways to use neural networks to detect objects is to train a classifier that characterizes each fragment of
the observed image as containing an object, or only a background. The size of the processed fragment is chosen equal
to the size of the image of the object. The detection procedure with this approach consists in sequentially picking
through all fragments of the image and checking them for the presence of an object using a trained classifier. For
detection, we used a three-layer convolutional neural network, schematically depicted in Figure 1.
Figure 1. Neural network
The first network layer convolves with 32 different filters of size 9x9 and reduces the size of the resulting images
by half. The reduction is carried out by selecting the largest element from a neighborhood of 2x2 pixels. The second
network layer similarly performed convolution with two filters of size 9x9 values and halving the size of the output
arrays. The third layer converts the resulting data array into one feature vector containing 1024 elements. The
resulting feature vector is then characterized as containing or not containing an object.
4 The combination of optimal linear filtering and neural network
Detecting objects using the method described above is rather computationally difficult, since each image fragment
must be processed by a neural network, which contains a cascade of a significant number of filters. The optimal linear
filtering method gives good enough results for a wide range of real backgrounds, while if the covariance matrix of the
background is estimated in advance, the calculation consists in filtering with a single linear filter. Thus, the idea arises
at the first stage of processing to use the optimal linear filter, and then apply the trained neural network. The
registered image can be represented in vector form as follows:
๐๐ ๐๐ = ๐๐ + ๐,
where ๐๐ is the vector of the object, ๐ is the vector of correlated noise (background). If ๐พ is the noise covariance
matrix, then the linear filter ๐, optimal in the sense of increasing the signal-to-noise ratio, has the form [3]:
๐ = ๐พ โ1 ๐๐ .
In practice, the matrix ๐พ, as a rule, is not known. In this work, we used a numerical estimate of the matrix K
obtained directly from the input images of the background. Having thus calculated the linear filter, further processing
can be carried out according to the scheme shown in Fig. 2.
Threshold Processing of
Optimal linear processing and suspicious Set of detected
filtration forming set of fragments by the objects
suspicious neural network
fragments
Figure 2. Combination of linear filtration and neural network
5 Source data and network training
For the experiments, we used images of the Earth from the Electro L-1 satellite available in the public
domain on the Internet [17]. In the work, point objects are considered, the dimensions and image shape of which are
determined by the system's hardware function. The shape of the object was modeled using the Gauss function, the
additive method of applying the object was applied. To train the network to recognize fragments after the filtering
procedure, the data was obtained as follows. A significant number of objects were applied to the original image at a
distance several times the size of the objects. Image fragments containing objects were saved and used to train the
network. A filter was built and the image was filtered with applied objects, as well as the original image without an
object. From the processed image, a brightness threshold was selected that determines the probability of detecting an
object and false alarm. Fragments were selected on the original image containing no objects, the response on the filter
in which exceeded the threshold value (false detected fragments). These fragments were subsequently used in training
the neural network as examples of a background containing no objects.
6 Experimental results
To compare the effectiveness of the optimal linear filtering and neural network, the following experiment was
carried out. One randomly selected background image was used to train the classifier; further comparison of the
algorithms was carried out on other background images. As an object, we used a Gaussian function with a maximum
intensity equal to one standard deviation of the background and parameter ๐ equal to 3. To obtain a test set of
fragments, 14,000 objects were applied to the background images. Fragments with printed objects were used to assess
the likelihood of detecting objects. To assess the likelihood of false alarm, 14,000 fragments of the same size were cut
out from the original image in arbitrary places. The resulting sets were processed by a trained classifier. The
processing results of several background images are shown in table 1.
Table 1. Comparison of neural network and optimal linear filtering
Texture Detection False alarm
probability
Net OLF
Background 1 0,9993 0,0057 0,0011
Background 2 0,9998 0,0061 0,0007
Background 3 0,9996 0,0085 0,0004
Background 4 0,9997 0,0055 0,0005
The โNetโ column of Table 1 shows the false alarm values when using the detection algorithm based on the
trained classifier, and the โOLFโ column - when using the optimal linear filtering. The table shows that in the
experiments the neural network showed results worse than the optimal linear filtering. Most likely this is due to the
fact that in the absence of a clear methodology, it is quite difficult to choose a training set to obtain a result close to
optimal. The data presented show that both algorithms give stable results when processing various input images.
Table 2 shows the results of an algorithm that combines optimal linear filtering and a neural network. In the
previous experiment, all fragments of the processed image were fed to the input of the neural network; in this
experiment, only fragments suspicious of the presence of an object according to the results of linear filtering. In this
case, the โBackground 4โ image was used with 900 printed objects. Experiments with other backgrounds gave similar
results. At the first stage, the optimal linear filtering algorithm was used, and the threshold values were selected that
give the detection probabilities indicated in the table in the column๐ผ1 . Each threshold value defines two sets: ๐ด1 - the
set of correctly detected objects, and ๐ต1 - the set of false detected fragments that do not contain objects. Denote ๐๐๐๐
- the number of all applied objects, ๐๐๐๐ฅ - the number of all pixels in the image. Using the sets ๐ด1 and ๐ต1 , the
probabilities of detection and false alarm were estimated using the optimal linear filtering algorithm shown in the
column โOLF1โ. The probability of detection was estimated as๐ผ1 = | ๐ด1 | / ๐๐๐๐ , the probability of false alarm ๐ฝ1 = |
๐ต1 | / ๐๐๐๐ฅ . Then the sets ๐ด1 and ๐ต1 were fed to the input of the neural network. The result is two sets: ๐ด2 - the set
of objects correctly classified by the neural network and ๐ต2 - the set of false fragments of the incorrectly classified
neural network as objects. The efficiency of the neural network when processing sets ๐ด1 and ๐ต1 , is shown in the
column "NeuralNet". It indicates the values ๐ผ๐ = |๐ด2 | / |๐ด1 | and ๐ฝ๐ = | ๐ต2 | / ๐ต1 , |. The total detection probabilities
and false alarms for the detection method considered are given in the โOLF + Networkโ column. It indicates the
values ๐ผ๐ถ = | ๐ด2 | / ๐๐๐๐ and ๐ฝ๐ถ = | ๐ต2 | / ๐๐๐๐ฅ . To compare the proposed approach, false alarm probabilities were
measured using the optimal linear filtering algorithm for the detection probabilities indicated in the column ๐ผ๐ถ . These
values are given in the "OLF" column and are designated as ๐ฝ0 .
Table 2. Combination of neural network and optimal linear filtering
OLF 1 NeuralNet OLF+Net OLF
๐ผ1 ๐ฝ1 ๐ผ๐ ๐ฝ๐ ๐ผ๐ถ ๐ฝ๐ถ ๐ฝ0
0,999 1,17*10-3 0,968 0,097 0,967 1,11*10-4 1,59*10-4
0,98 1,93*10-4 0,969 0,404 0,95 7,56*10-5 1,27*10-4
0,96 1,38*10-4 0,971 0,480 0,932 6,62*10-5 1,07*10-4
0,94 1,16*10-4 0,976 0,5 0,918 5,61*10-5 9,92*10-5
0,92 1,0*10-4 0,979 0,545 0,901 5,29*10-5 9,11*10-5
0,90 9,03*10-5 0,980 0,564 0,882 4,94*10-5 8,13*10-5
When comparing the values of ๐ฝ๐ถ and๐ฝ0 , it can be seen that the proposed approach allowed us to reduce the
probability of false alarm by 40-60 percent, with the same probability of detection. The nature of the changes in the
values of ๐ผ๐ and ๐ฝ๐ shows that the results of detection using a neural network correlate with the results of detection
by the optimal linear filtering algorithm. To obtain lower values of ๐ผ1 , it is necessary to use a higher threshold at the
stage of threshold processing, which gives sets ๐ด1 and ๐ต1 , containing fragments with a higher intensity of the
response to the filter. Since the main sign of the presence of an object is an additional registered intensity, it can be
assumed that the set of true objects with a higher intensity ๐ด1 becomes easier for correct recognition, and the set of
false fragments with a higher intensity ๐ต1 becomes more complicated. This can explain the nature of the changes in
the quantities ๐ผ๐ and ๐ฝ๐ . The decrease in ๐ฝ๐ถ with respect to ๐ฝ0 is most likely due to the fact that the neural network
uses additional features to the filter response that can be used to improve the final results.
7 Conclusion
In the experiments performed, the direct use of a neural network to classify fragments in the considered
range of detection probabilities did not improve the results obtained by the optimal linear filtering method. At the
same time, the ability to effectively use a combination of optimal linear filtering and a neural network has been
shown. Because of applying the proposed approach, the detection efficiency of objects was increased; the probability
of false alarm was reduced by 40-60 percent with the same probability of detecting an object. Further research may be
aimed at more precise adjustment of network parameters and the use of large amounts of data in the learning process.
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