Method for Obtaining Shadow Images of Control Objects for Telemetric Care Systems Lidiia Tereshchenko1 1 National Aviation University, 1 Lubomyr Huzar ave., Kyiv, 03058, Ukraine Abstract 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 Neyman- Pearson criterion. Analysis shows that the proposed spectral detector has good operating characteristics even at low signal-to-noise ratios. Keywords 1 Keywords: aviation security service, X-ray, optical imaging, shadow of three-dimensional objects, spectral detector. 1. Introduction 2. Problem Statement Ensuring effective protection against terrorism The paper addresses applied research is the most difficult issue, especially for countries challenges concerning the development and with a developed air transport network, a large application of a new method of determination number of airlines, and airports. The problem is (visualization) of the internal structure of the complicated by the unpredictability of terrorists’ Objects Under Control (OC), that enables actions. In addition, vulnerabilities in aviation dangerous OC to be identified with high security systems (such as procedures for screening probability in real-time, increases the speed of airline passengers and their baggage, freight dangerous substances identification in luggage, shipments, mail, etc.) that can be exploited by law and provides automation of these processes. In violators should be taken into consideration. The addition, the automatic generation of images of main way to improve aviation safety is to prevent hazardous OC allows for periodic inspections of hazardous objects and substances, explosive aviation security service operators. Detection devices, and weapons on aircraft boards. This systems based on X-ray, computer tomography, requires a comprehensive development and and spectroscopy of mobile ions have certain introduction of new methods of screening, shortcomings [3–9]. Some of these systems can detection, and identification of dangerous objects detect well-hidden explosives, but their under control. Insights of the direct visualization implementation requires considerable funds. In methods indicate that they are inherent in the same addition, they have a high level of false alarms type of operations: primary radiation exposure of (approximately 0.2 ... 0.4). Thus, the development the objects under control in configuration space of analytical models for the receipt of (in the case of active method), reradiation multidimensional shadows of translucent objects reception (scattered or passed through the object), for further processing will allow the classification its conversion into an electrical signal, signal of OC, which will greatly facilitate the work of processing and electrical-to-optical signal operators serving supervision devices in Aviation conversion [1, 2]. Security Service (AvSS), reducing the value of false alarms. Literature analysis showed that the CPITS 2023: Workshop on Cybersecurity Providing in Information and Telecommunication Systems, February 28, 2023, Kyiv, Ukraine EMAIL: 10118@ukr.net (L. Tereshchenko); ORCID: 0000-0001-8183-9016 (L. Tereshchenko); ©️ 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) 191 modernization of equipment for AvSS is carried irradiation by a point source located on the axis of out in two directions: in the part of the object symmetry perpendicular to the plane of the improvement of hardware and software. In [10] image (screen). To determine the position of the authors proposed a new X-ray backscatter radiation source, the OC, and the screen with a technique using an un-collimated powerful (high point source it is appropriate to use the cylindrical kW) X-ray beam and an efficient pinhole camera coordinate system applied to the Fig. 1. The OC encompassed with a high-resolution matrix model with complex form is presented in Fig. 2. detector for imaging of an object. Moreover, a high-energy X-ray inspection technique for the reliable inspection of air freight containers was presented in [11]. Analysis of various strategies for object detection in X-ray security imagery is given in [12]. Moreover, the paper [13] also deals with a technique for the classification of X-ray baggage images using convolutional neural networks. The application of deep convolutional neural network as a classification method in Figure 1: OC scanning: (а) is the setting of a medicine X-ray image analysis was considered in [14]. cylindrical coordinate system; (b) is the setting of In [15] authors investigated the feasibility a scanning beam position of applying straight-line-trajectory-based tomographic imaging configurations to security inspections. The method of automated target recognition with the usage of a reference database, which contains X-ray images of OC, for cargo scanning systems was proposed in [16]. The papers [17, 18] deal with procedures of handguns, shuriken, and razor blades recognition for baggage inspection. The simulation of the internal structure for OC with simple and complex forms using the point source of irradiation in the center, as well as with the bias relative to the center, is considered in [19]. The method developed for optical imaging of the inner structure of the three- dimensional objects allows obtaining a shadow of Figure 2: OC with complex form these objects, exposed to electromagnetic radiation. It has useful applications in different Internal visualization of the OC with a life spheres, such as in medicine, the complex form, in this case, a sphere in the sphere, manufacturing industry, the process of customs designed with a point source is shown in Fig. 3. supervision of goods and means of transport for commercial use, etc. It allows the AvSS to increase the probability of correct detection of hazardous materials and reduce false alarms in its security system. For medicine, the method may help to increase the probability of health hazard anomaly detection. So aim of this paper is a synthesis of a two-dimensional spectral detector for baggage inspection X-ray devices. 3. Materials and Methods The construction of an analytical model reduces to the calculation of a projective image of an isotropic object in the case of homogeneous Figure 3: Inner structure imaging for OC 192 The simulation shows that the simplest objects have shadows with transient characteristics, half- dooms, 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 Figure 4: Object of complex shape source, the OC and the screen receiver, the irradiation angles, etc. Methods of analytical Objects marked with stars are not graphs, but modeling of the OC with different shapes, drawings illustrating examples of corresponding geometrical dimensions, foreshortening, graphs with the following input data: k=10; a1=2; substance, and appropriate extinction coefficients, b1=4; c1=1; d1=1; d2=1; 1 = 1;a2=1; b2=5; c2= 3; 2 = 1 . The following formulas calculate the used to develop procedures for identifying dangerous objects under security supervision of imaginary distribution of the visualized parameter passengers and baggage, allow imaging of OC's inner structure. To verify the developed models with logarithmic gain. b(x, h ) = artg multidimensional spectra of visualization images h are obtained. The procedure for image processing x consists of using a shadow of the object of a given X 2(x, h ) = x 2 + h 2 shape to construct a two-dimensional spectrum and its subsequent use in developing the standard  b1  g1 = atg  spectral detector proposed in the research. This  a1  detector is invariant concerning the location of the  b2  OC in the working area. The invariance of the g 2 = atg  calculated spectrum to the location of the OC on  a2  the plane of the screen provides the possibility of applying algorithms for the calculation of two- dimensional 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—Fourier- image М ( К x , K y ) . In the further processing of Figure 5: Image of the internal structure of a complex OC with applied parameters in three- visualization data, we find solutions in the dimensional form frequency space М ( К x , K y ) , and then, through Projective image OK with logarithmic gain. 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. Figure 6: Projective image of OK with logarithmic amplification 193 The function corresponding to the intensity distribution of the received radiation is obtained by the formula: d ( x, h ) = e − a ( x , h ) Figure 7: Image of the internal structure of a complex OK with applied parameters, in three- dimensional form Consider the object of control in the form of a Figure 9: Image of the internal structure of a pipe segment with a cavity inside. complex control object with applied parameters, Let’s set the parameters of the rendering in three-dimensional form 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:  ( 0 if − x 2 + y 2  r1  x 2 + y 2  −   r 2  − x 2 + y 2  x 2 + y 2  r 2   F1(x, y ) =  )  d Figure 11: Shadow (a) of a parallelepiped and its spectrum (b) Figure 8: Object Figure 12: Shadow (a) of the cylinder and its F1 r 2k spectrum (b) OD 2 = c+d . On one plane, the shadows of two X 2(x, h ) = x + h , OD2 = r 2k ; 2 2 parallelepipeds are located, and their spectral c+d images are obtained (Fig. 13). a(x, h ) = (a p (x, h ) − av (x, h ))a . 194 probability of correct detection of a signal from an OC. Figure 13: Shadows of two parallelepipeds and their spectrum: a) shadows of two parallelepipeds; b) a three-dimensional image of Figure 15: Model of shadow OC the spectrum of those shadows; c) a two- dimensional projection of the spectrum of A mixture of useful signals and noise is shown shadows of parallelepipeds in Fig. 15. A mixture of signal with noise in cases of signal-to-noise ratios equaled to 2 (a) and 0.5 The following figures show the spectral (b) The Neyman-Pearson criterion is applied for images of the shadows of the parallelepiped and optimal detection of an OC. According to the the spheres that were located in space (Fig. 14). 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 Figure 14: Shadows of parallelepiped and program calculates the characteristics of the spheres and the spectrum of their compatible detection. An example of these characteristics is shadows: a) shadows; b) a three-dimensional shown in Fig. 10. On these graphs it is seen that image of the spectrum of those shadows; c) a two- when the decision threshold is reduced, the detection characteristic is more efficient, dimensional projection of the spectrum of shadows however, the probability of false detection is Analysis of the spectra of hazardous and forbidden increased. The analysis shows that the developed OC allows us to create an appropriate database for spectral detector has good detection the further detection of OC of various shapes and characteristics even at low signal-to-noise ratios. complexity 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 Figure 16: Characteristics of signal detection for boundaries. One object is a regular square (this kind sample size 1000 and probabilities of false alarms can have dynamite), and the other is a model of the F = 0.05 and F = 0.03 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 4. Conclusions an OC with a given probability of false alarms for the corresponding threshold decision depending on The analysis of scientific publications has the size of the OC. The program calculates the shown that the most effective methods for the detection and identification of hazardous OCs are 195 transient multi-energy direct X-ray ones. 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