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.
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.
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. 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
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:
= + , = −1 .
matrix, then the linear filter , optimal in the sense of increasing the signal-to-noise ratio, has the form [3]: where is the vector of the object, is the vector of correlated noise (background). If is the noise covariance In practice, the matrix , 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.
processing and forming set of suspicious fragments
objects
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
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 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.
The “Net” column of Table 1 shows the false alarm values when using the detection algorithm based on the trained classifier, and the “OLF” 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 “Background 4” 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 column 1. Each threshold value defines two sets: 1 - the set of correctly detected objects, and 1 - the set of false detected fragments that do not contain objects. Denote - the number of all applied objects, - the number of all pixels in the image. Using the sets 1 and 1, the probabilities of detection and false alarm were estimated using the optimal linear filtering algorithm shown in the column “OLF1”. The probability of detection was estimated as 1 = | 1 | / , the probability of false alarm 1 = | 1 | / . Then the sets 1 and 1 were fed to the input of the neural network. The result is two sets: 2 - the set of objects correctly classified by the neural network and 2 - the set of false fragments of the incorrectly classified neural network as objects. The efficiency of the neural network when processing sets 1 and 1, is shown in the column "NeuralNet". It indicates the values = | 2| / | 1| and = | 2 | / 1, |. The total detection probabilities and false alarms for the detection method considered are given in the “OLF + Network” column. It indicates the values = | 2 | / and = | 2 | / . To compare the proposed approach, false alarm probabilities were measured using the optimal linear filtering algorithm for the detection probabilities indicated in the column . These values are given in the "OLF" column and are designated as 0.
When comparing the values of and 0, 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 and 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 1, it is necessary to use a higher threshold at the stage of threshold processing, which gives sets 1 and 1, 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 1 becomes easier for correct recognition, and the set of false fragments with a higher intensity 1becomes more complicated. This can explain the nature of the changes in the quantities and . The decrease in with respect to 0 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
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