The paper deals with two-dimensional spectral detectors for baggage inspection X-ray devices. This detector is based on the construction of analytical models for the internal structure of objects under control and their spectrum calculation. The methods of projective geometry and Bouguer-Lambert law are applied to obtain the analytical models for shadows of three-dimensional objects. Spectral detectors are designed according to the NeymanPearson criterion. Analysis shows that the proposed spectral detector has good operating characteristics even at low signal-to-noise ratios.
Ensuring effective protection against terrorism
is the most difficult issue, especially for countries
with a developed air transport network, a large
number of airlines, and airports. The problem is
complicated by the unpredictability of terrorists’
actions. In addition, vulnerabilities in aviation
security systems (such as procedures for screening
airline passengers and their baggage, freight
shipments, mail, etc.) that can be exploited by law
violators should be taken into consideration. The
main way to improve aviation safety is to prevent
hazardous objects and substances, explosive
devices, and weapons on aircraft boards. This
requires a comprehensive development and
introduction of new methods of screening,
detection, and identification of dangerous objects
under control. Insights of the direct visualization
methods indicate that they are inherent in the same
type of operations: primary radiation exposure of
the objects under control in configuration space
(in the case of active method), reradiation
reception (scattered or passed through the object),
its conversion into an electrical signal, signal
processing and electrical-to-optical signal
conversion [
The paper addresses applied research
challenges concerning the development and
application of a new method of determination
(visualization) of the internal structure of the
Objects Under Control (OC), that enables
dangerous OC to be identified with high
probability in real-time, increases the speed of
dangerous substances identification in luggage,
and provides automation of these processes. In
addition, the automatic generation of images of
hazardous OC allows for periodic inspections of
aviation security service operators. Detection
systems based on X-ray, computer tomography,
and spectroscopy of mobile ions have certain
shortcomings [
In [
The construction of an analytical model reduces to the calculation of a projective image of an isotropic object in the case of homogeneous irradiation by a point source located on the axis of object symmetry perpendicular to the plane of the image (screen). To determine the position of the radiation source, the OC, and the screen with a point source it is appropriate to use the cylindrical coordinate system applied to the Fig. 1. The OC model with complex form is presented in Fig. 2.
Internal visualization of the OC with a complex form, in this case, a sphere in the sphere, designed with a point source is shown in Fig. 3.
The simulation shows that the simplest objects have shadows with transient characteristics, halfdooms, and distortions of the type of crater, where there are generally flat irradiating planes. Changing the irradiation angle changes the shadow to unrecognizability. To accurately identify the intended OC, it is necessary to automate the process of recognizing shadows, taking into account possible distances between the source, the OC and the screen receiver, the irradiation angles, etc. Methods of analytical modeling of the OC with different shapes, geometrical dimensions, foreshortening, substance, and appropriate extinction coefficients, used to develop procedures for identifying dangerous objects under security supervision of passengers and baggage, allow imaging of OC's inner structure. To verify the developed models multidimensional spectra of visualization images are obtained. The procedure for image processing consists of using a shadow of the object of a given shape to construct a two-dimensional spectrum and its subsequent use in developing the standard spectral detector proposed in the research. This detector is invariant concerning the location of the OC in the working area. The invariance of the calculated spectrum to the location of the OC on the plane of the screen provides the possibility of applying algorithms for the calculation of twodimensional spatial spectra of the visualization image about the wanted images of some image anomalies in the endoscopic imaging systems of the AvSS. That is, the desired density distribution of the object of control μ(x, y) must be matched to fit its two-dimensional spatial spectrum—Fourierimage М (К x , K y ) . In the further processing of visualization data, we find solutions in the frequency space М (К x , K y ) , and then, through the inverse Fourier transform, the desired distribution is calculated μ*(x, y), . The resulting distribution is selected according to those images, which are in the memory of the supervision system. A decision is made to detect a particular object after matching the resulting image μ*(x, y) and mask μ*(x, y).
Figs. 4 and 5 shows the spectra of images of different shades of opaque OC of a simple shape on the size of a 100×100 screen plane located almost above the center of the screen.
Objects marked with stars are not graphs, but drawings illustrating examples of corresponding graphs with the following input data: k=10; a1=2; b1=4; c1=1; d1=1; d2=1; 1 = 1;a2=1; b2=5; c2= 3; 2 = 1 . The following formulas calculate the imaginary distribution of the visualized parameter with logarithmic gain. h x b(x, h) = artg
The function corresponding to the intensity distribution of the received radiation is obtained by the formula:
d (x, h) = e −a( x,h )
Consider the object of control in the form of a pipe segment with a cavity inside.
Let’s set the parameters of the rendering system:
r1 = 3, r2 = 2, k = 10, d = 1, c = 1, a = 1 where k is the distance from the radiation source to the screen; c is the distance from the radiation source to the OK; r1 is radius OK; r2 is cavity radius; d is layer thickness; a is the radiation attenuation coefficient in the OK material.
The actual distribution of the extinction coefficient will be:
On one plane, the shadows of two parallelepipeds are located, and their spectral images are obtained (Fig. 13).
The following figures show the spectral images of the shadows of the parallelepiped and the spheres that were located in space (Fig. 14).
When using X-ray systems to provide automation of care and increase the reliability of decision-making on the presence of prohibited articles and substances in the OC, there are problems in identifying different forms and locations of the OC. For this purpose, the example of the spectral detector model was constructed in the Matlab environment. In this case, the detection occurs regardless of the OC location and regardless of its shape and size. The considered models are the shadows of two objects in a field with specified boundaries. One object is a regular square (this kind can have dynamite), and the other is a model of the machine gun (Fig. 15). Also, white Gaussian noise and a mixture of image and noise are modeled (Fig. 16). The developed program allows us to detect an OC with a given probability of false alarms for the corresponding threshold decision depending on the size of the OC. The program calculates the probability of correct detection of a signal from an OC.
A mixture of useful signals and noise is shown in Fig. 15. A mixture of signal with noise in cases of signal-to-noise ratios equaled to 2 (a) and 0.5 (b) The Neyman-Pearson criterion is applied for optimal detection of an OC. According to the Neyman-Pearson criterion, the threshold level V is determined from the condition that the probability of a correct detection D with the given probability of false alarm F was maximal. Hence, the optimal character of the Neyman-Pearson criterion is that it maximizes the probability of correct detection at a fixed probability of false alarms. In addition, it should be noted that the program calculates the characteristics of the detection. An example of these characteristics is shown in Fig. 10. On these graphs it is seen that when the decision threshold is reduced, the detection characteristic is more efficient, however, the probability of false detection is increased. The analysis shows that the developed spectral detector has good detection characteristics even at low signal-to-noise ratios.
The analysis of scientific publications has shown that the most effective methods for the detection and identification of hazardous OCs are transient multi-energy direct X-ray ones. They provide reliable detection of hazardous OCs. However, these methods are complicated, their implementation in the supervisory systems has a significant expenditure of material resources, and they do not work efficiently with dynamic OCs. At a high probability of correct detection to 0.99, there is a high probability of false alarms from 0.3 to 0.4. The simulation shows that the simplest OC has shadows with transient characteristics, halfdooms, and distortions of the type of crater, where there are generally flat irradiating planes. Changing the irradiation angle changes the shadow to unrecognizability. To accurately identify the intended OC, it is necessary to automate the process of recognizing shadows, taking into account possible distances between the source, the OC and the screen receiver, the irradiation angles, etc. The procedure for image processing consists of using a given shape OC shadow to construct a two-dimensional spectrum and its subsequent use in developing the standard spectral detector. This detector is invariant concerning the location of the OC in the working area. To solve the problem, a spectral detector model is developed using the MatLab software environment. In this case, the detection occurs regardless of the OC location or its shape and size. It allows the detection of dangerous objects with a high probability of correct detection and a low probability of false positives (from 0.03 to 0.05).