This work is aimed at comparing the classification algorithms and methods of machine learning with various methods of preliminary processing of radar images. Preprocessing step includes speckle noise filtering and object orientation normalization on the image. In comparison, the following classification algorithms were considered: Decision Tree, Support Vector Machine, K Nearest-Neighbor method, Random Forest, AdaBoost where decision tree was used as a weak classifier, Convolutional Neural Network and Residual Neural Network. The principal component analysis was applied to reduce the dimension. The study was carried out on the objects from the base of radar images MSTAR.
Radar satellite imagery obtained with synthetic aperture radar received its distribution due to independence from weather and natural illumination. The recognition of objects on radar images is used in various fields, such as agriculture, forestry, geology, ecology, and also in the work of the emergency and rescue services. Synthetic aperture radar is usually an air or space radar system that uses the flight path of a platform to simulate an extremely large antenna, which makes it possible to create images of remote sensing of the earth with high resolution.
A certain complexity in the processing of the images obtained is the speckle noise that is present on the radar images. To improve the accuracy of the classification of images, the orientation of the object is also normalized. In most cases, the angle of rotation of the target is unknown. In this paper, we consider three methods commonly used in scientific articles to find the angle of rotation: a method that relies on the use of image moments; a method based on the Hough Transform, in which there is a search for long straight lines in the image, which are taken beyond the boundaries of the object; a method based on finding a rectangle with a minimum area describing the object.
The paper compares classical algorithms for the classification of radar images for various methods
of their preliminary processing and methods based on the use of convolutional neural networks [
The paper is organized as follows. In the second section, the statement of the classification problem is given. The third paragraph describes methods of preliminary image processing and compares the accuracy of finding the angle of rotation. In the fourth chapter, a method for reducing the dimensionality of the characteristic space is described. In the fifth chapter, the classification algorithms under investigation are described. The sixth chapter presents the results of experimental studies. The conclusion contains conclusions and plans for further research. In the end of the work, thanks and a list of used literature are indicated.
The task of object recognition on an image can be divided into two main subtasks:
- search for an object in the image and selection of areas of interest;
- recognition and classification of the found object or area of interest. [
The first subtask is aimed at finding objects for classification. Often information about the location, size, orientation, availability, and a number of goals is initially missing. In this case, it is necessary to determine the unknown parameters required for further selection of the object or local area of interest.
The second subtask is applied to the entire image and allows you to decide which of the several classes the image being processed belongs to. The decision function for each feature vector relates the object to the corresponding class. In this paper, we consider only the classification problem.
Due to the need to process a large number of images for training and testing, as well as a low
performance of some algorithms, there is a need to reduce the dimensionality of the feature space.
There are various methods used to solve this problem. These methods include the most popular
methods: the principal component analysis, factor analysis, the independent component analysis,
Selforganizing map and others. In article [
using the following formula, where 1′1 = 11/ 00 = 11/ 00 − , 2′0 = 20/ 00 = 20/ 00 − 2, 0′2 = 02/ 00 = 02/ 00 − 2: The preliminary processing of images consists of two stages. At the first stage, speckle noise is filtered by the Lee filter and threshold processing. At the second stage, one of the methods of normalizing the orientation of the object on the image is applied.
The method based on the moments of the image allows us to obtain the required rotation angle = 1 2
2 1′1 arctg 2′0+ 0′2 + 2 ( = 0,1, … ) (1)
In the method based on finding the minimum area of the rectangle describing the object in the image, the rotation angle is calculated as the angle between the horizontal and one of the sides of the rectangle. It is assumed that the rectangle will describe the object on the image in such a way that the longest side of the object will be described by the long side of the rectangle. To isolate the boundaries of an object, the Canny algorithm is used. The objects from the MSTAR database, described by the minimum area rectangle are shown in Figure 1.
The method based on the Hough Transform involves finding long straight lines on the image that can be the boundaries of the object. The rotation angle is calculated for the line corresponding to the longest, straight and continuous face of the object. Like the previous one, this method is suitable for normalizing the orientation of an object with direct boundaries. To isolate boundaries, one can use the Canny algorithm or the Sobel operator. Figure 3 shows the scheme of the preliminary processing algorithm with the described method.
An example of this method is shown in Figure 4.
Table 1 shows the percentage of the number of images deviated from the true rotation angle by a specified angle to the total number of images.
The images obtained after normalization of the object are cut off. fourth demonstrate the correct operation of the method.
Principal Component Analysis (PCA) is one of the most widely used methods for reducing the
dimensionality of a feature space with the loss of the least amount of information. This method
reduces to calculating the eigenvalues of the covariance matrix of the analyzed image. [
5.1. K-Neighbors training sample is maximal: K-nearest neighbors algorithm refers to metric classification algorithms with training sample ΩO. Such algorithms refer object to that class ∈ Y, for which the total weight of the nearest objects from the ( , ΩO) = max ∈ Γ ( , ΩO), и Γ ( , ΩO) = ∑K=1 [ ( ) = ] ( , ), (2) ()
where the weight function (, )
estimates the degree of importance of the -th neighbor for the classification of the object . The function Γ (, Ω O)is an estimate of the closeness of the object to the class . The importance function is chosen to be non-negative and not increasing in . The selection criteria are due to the fact that the smaller the distance between the sampled objects and , the greater the probability of a correct classification. In the algorithm of the nearest neighbors, the object is referred to a class with more elements among the nearest neighbors (, ) = [ ≤ ] , (, Ω O, ) = max ∈ ∑ =1 [ ( ) = ] .
() , = 1, :
The article used the Minkowski metric. It can be regarded as a generalization of the Euclidean and Manhattan distances. For the parameter = 2 , the Minkowski distance is generalized to the Euclidean distance, and for p = ∞- to the Chebyshev distance. This metric is defined by the following formula: The drawbacks of metric algorithms include storage of the entire training sample.
(, ) = (∑=1 | − | ) ⁄ .
1
Decision Tree is a structure of a hierarchical type, in which branches a partition of the feature space is
defined, and the sheets are elementary classification functions. There are various methods for
constructing trees. In this paper, the algorithms C4.5 [
C4.5 builds the source tree based on the input sample ΩO. If all objects in the sample belong to the same class or the sample is small, then the tree is a sheet marked with the most common class in the sample. Otherwise, a split criterion is selected that divides the sample into two or more samples. Then the criterion is chosen for the obtained partitions. This procedure is recursively applied to each sample received. One of the criteria used, which is used in the work, is to minimize the entropy value of the obtained sample partitions. The resulting source tree is then trimmed to avoid retraining. Based on the received tree, a decision function is constructed for classifying objects.
In the CART algorithm, a binary decision tree is recursively constructed. The tree is created to the
maximum size without using the stopping rule, and then it is clipped. The algorithm builds not one but
a sequence of nested truncated trees. The best division is selected based on the sliding control. The
partition criterion is based on the Gini index.
5.3. SVM
The support vector machine is one of the most reliable methods among all known algorithms and is
most often used for comparison with new algorithms. The function separating the classes is a
separating hyperplane. The algorithm maximizes the shortest distance between the points closest to the
points on the hyperplane [
A popular boosting algorithm AdaBoost was suggested by Freund and Schapire [
Random Forest is a set of decision trees. The decision to classify is made by voting the majority. Each decision tree is built independently of the others. For each tree, a subsample of the training sample is selected. For splitting the tree, the best attribute is selected. Typically, the tree is built before the exhaustion of the sample, the leaves of the tree should contain representatives of only one class.
A convolutional neural network (CNN) consists of one or more convolutional layers and subsequent one or more fully connected layers. CNN is often used to recognize objects, images, as well as to detect and segment objects. The use of GPUs made it possible to significantly accelerate the training of the neural network and to reduce the time for conducting experimental studies. Classification algorithms based on convolutional neural networks make it possible to achieve better results in image recognition and stability to rotate and shift the object in the image.
Residual networks allow the construction of much deeper networks than conventional convolutional
networks. The article [
The residual neural network consists of residual blocks, including a pair of layers, where the input of the first layer is added to the output of the second layer. Figure 5 shows the residual block.
To assess the results of the classification, the sliding control method is used. Cross-validation is a statistical method for assessing the generalization of the quality of classification. It is a more reliable and thorough assessment method, compared to the usual sequential division of a data set into a training and test sample. With cross-validation, the data is repeatedly divided into training and test sets and fed to the classifier's input.
The paper uses a modified method of sliding control with multiple partitioning [
N ≥ K + L, ΩO ∪ ΩT = Ω′, Ω′ ⊆ Ω, ΩO ∩ ΩT = ∅, ΩO = ⋃K=−01 ΩO , ΩT = ⋃L=−01 ΩT (5) Where ΩO is a training sample, ΩT is a test sample, Ω is the original sample.
For each partition obtained, the classifier is set up on the training sample and the quality value of the classifier is calculated on the test sample.
The functional quality of the algorithm on the sample has the following form:
CV(μ, Ω′) = N1 ∑N=1 N1 ∑N=1 Q(μ(Ω′\ΩO ), ΩO ), (6) where μ is the learning method.
All the experimental studies were conducted on Intel Core i5-6600, 16 GB of RAM, NVIDIA GeForce GTX 970. All classification algorithms were written in Python 3.6. Also used were frameworks and libraries scikit-learn, scikit-image, openCV, numpy, tflearn, tensorflow. As objects of classification, samples of military equipment from the public database of radar images MSTAR.
For recognition, the magnitudes of the images of BMP-2, BTR-60, BTR-70 and T-72 were used. Prior to the classification, preliminary processing and cropping of images to a size of 60×60 pixels described in paragraph 3 was carried out. Classification by neural networks was carried out without preliminary image processing.
The target shooting angle is 15 and 17 degrees. The initial sample consists of 3438 images. For all images from the general sample, the dimension was reduced.
The value of the classification quality will be calculated as the average relative number of correctly
classified objects from the test sample ΩT. For the sliding control method, we specify the number of
partitions and the number of iterations N = 10, K = 6 and L = 4, dividing the total sample in the ratio
6:4. The method of the main components will reduce the dimensionality, retaining a significant part of
the radar image information necessary for the classification of objects. The results of the
classification, together with the results obtained in [
The algorithms AdaBoost and Random forest significantly outperformed the results of CART and C4.5. Perhaps a further selection of parameters will help to achieve values that showed the method of nearest neighbors and the method of support vectors. Although the method based on Hough Transform showed the smallest average deviation of the obtained angle from a known value, the accuracy classification with this pre-treatment method gave way to the classification accuracy using the other two methods because of the high mean square deviation. Сlassifier KNeighbors CART C4.5 SVM AdaBoost Random forest CNN ResNet
Image moments
Classification algorithms based on the use of convolutional neural networks have surpassed the other classification algorithms studied in the case of methods of object orientation normalization. The method of nearest neighbors and the method of support vectors for a known angle of rotation of the target show a similar classification accuracy. Due to the fact that in practical classification tasks the angle of object rotation is rarely known, the application of classification algorithms based on convolutional neural networks will allow achieving better results even without preliminary image processing.
In this paper, we compare the classification algorithms in the problem of object recognition on radar images. Various methods of preliminary image processing and object orientation normalization were presented and studied. The experimental studies carried out have shown the dependence of the classification accuracy on the value of the root-mean-square deviation of the image rotation angle. It is shown that the application of classification algorithms based on convolutional neural networks allows obtaining the best classification accuracy even without preliminary image processing.
A further area of research is the development of a classification algorithm based on a convolutional neural network and the selection of the best hyperparameters, which allows to exceed the obtained classification accuracy.
This work was supported by the Russian Foundation for Basic Research (RFBR) grant 17-29-03190, 18-01-00748 A and by the Federal Agency of scientific organization (Agreement 007-GZ/43363/26).