The present work is devoted to the analysis of local objects on radar images. In comparison, the following algorithms are used: decision tree; Bayesian classifier for normal distribution; Nearest neighbor method; Support Vector Method (SVM). As preliminary processing of images provided by a synthetic aperture radar. The research is carried out on the objects from the base of radar images MSTAR. The paper presents the results of the conducted studies. Radar satellite imagery obtained with synthetic aperture radars allows obtaining images of good quality in difficult weather conditions, as well as in cases of low illumination. A certain complexity in the processing of the obtained images is the speckle noise that is present on the radar images. The recognition of images on radar images is used in various fields, such as agriculture, forestry, relief analysis, oil spill monitoring and equipment recognition. Studies of various algorithms for the classification of radar images has been conducted previously, but often they had been compared the obtained data with the data from other articles. Such an approach may lead to inaccurate results of the analysis of the results obtained. Also, most articles use for comparison only the most popular classification algorithms, such as SVM, AdaBoost and neural networks. In this paper, the study adopted classifiers, which are used in works on this topic less often: decision trees, k nearest neighbors method, naive Bayesian classifier. The purpose of this paper is to fill this gap. All tests were conducted using the public database of radar images of MSTAR military equipment.
The Principal Components Analysis (PCA) method 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. [
To assess the results of the classification, the sliding control method is used. Sliding control (cross-validation, CV) 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 the sliding control, 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 [
ΩT .
K−1 ⋃
̂ = max ( ) ∏ ( | ).
=1 ( | ) =
1 √2 2 (−( − )2
) 2 2 and use the a posteriori maximum estimate to estimate ( ) and ( | ).
Naive Bayesian classifiers differ, mainly, by the assumptions they make about ( | ).
In this paper, the densities used are the Gaussian case, which is based on the use of the probability density of the form: where and 2 are the mathematical expectation and the correlation matrix.
The nearest neighbor's 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 training sample is maximal: ( , ΩO) = max ∈ Γ ( , ΩO), и Γ ( , ΩO) =
K ∑ ( ) = ] ( , ). is referred to a class with more elements among the nearest neighbors ( ), = 1, :
Where the weight function ( , ) estimates the degree of importance of the -th neighbor for the classification of the object objects and . The function Γ ( , ΩO)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 ( ), the greater the probability of a correct classification. In the algorithm of the nearest neighbors, the object ( , ) = [ ≤ ] , ( , ΩO, ) = max ∈
∑ ( ) = ] .
As a metric, the Euclidean metric is most often chosen because of its simplicity and comprehensibility. Three metrics are studied: Euclidean, Minkowski and Manhattan distance.
The Euclidean distance between two points , is defined in Euclidean n-dimensional space as: ( , ) = √( 1 − 1)2 + ( 2 − 2 )2 + ⋯ + ( − )2 = √∑( − )2 .
=1 The Manhattan distance is defined as the sum of the moduli of the coordinate differences: ( , ) = ‖ ⃗ − ⃗‖ =
∑ =1 | − |.
Another metric on the Euclidean space, which is investigated in the paper is 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: ( , ) = (∑ =1 | − | ) ⁄ .
1 The drawbacks of metric algorithms include storage of the entire training sample.
A 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 algorith ms
C4.5 [
C4.5, receiving the input sample ΩO, builds the source tree, based on the following rules. 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 for each sample received. One of the criteria is used 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 b est division is selected based on the sliding control. The partition criterion is based on the Gini index.
5.4. 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 [
served. images are shown in Figure 2.
All the experimental studies were conducted on a PC Intel Core i5-4460, 16 GB RAM. All classification algorithms were written in the programming language Python 3.6. Also used were frameworks and libraries scikit-learn, openCV, numpy. As objects of classification, samples of military equipment from the public database of radar images MSTAR, presented in Figure 1,
For recognition, the magnitudes of the images of BMP-2, BTR-60, BTR-70 and T-72 were used. As preprocessing of images, the orientation of objects on centered images was normalized and cropped from 128 × 128 to 60 × 60 pixels. The resulting
The target shooting angle is 15 and 17 degrees. The initial sample consists of 3438 images of different classes of objects. The number of images of each class is shown in Table 1. For all images from the general sample, the dimension was reduced. The list of investigated classifiers is given in Table 2.
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 dimension to 20 eigenvectors, retaining a significant part of the radar image information necessary for the classification of objects. Detailed classification results are presented in Table 3.
The support vector machine with a radial basis function and the k nearest-neighbor method (with Minkowski distance) showed the best result of the classification of radar images.
It can be seen from the results of the conducted research that the best indicators of the classification of radar images of t he
MSTAR base are given by the method of the nearest neighbors, and by the support vector machine. In subsequent studies, it is
planned to apply boosting algorithms, such as AdaBoost [