A method for estimating RCS of targets at all angles based on image extraction and electromagnetic simulation

Abstract

The present invention discloses a method for estimating the RCS of a target at all angles based on image extraction and electromagnetic simulation. The method uses region delimitation and scattering point integration techniques to calculate the target's true RCS. Using electromagnetic calculation methods, a 3D model of the target is input, specifying the same imaging angle as the image slice, to obtain the scattered field intensity of the target's echo, and then calculate the target's simulated RCS. A conversion function between the actual RCS and the simulated RCS is established through function fitting. A two-dimensional simulated RCS table is calculated using electromagnetic simulation technology, and converted into a modified simulated RCS table using the RCS conversion function. For any given imaging angle, the corresponding position is searched in the modified simulated RCS table, and the estimated RCS value at that imaging angle is obtained using bilinear interpolation. Using the modified simulated RCS table, the present invention can accurately estimate the target RCS at any imaging angle.

Description

Technical Field

[0001] The present invention belongs to the technical field of Synthetic Aperture Radar (SAR) remote sensing image processing and electromagnetic simulation, and relates to a method for estimating the RCS of a target at an unknown angle by using the backscatter cross-section (RCS) of the target at a known angle. Specifically, the present invention relates to a method for estimating the RCS of a target at an unknown angle by extracting the target RCS from an image and calculating the target RCS through electromagnetic simulation, and obtaining the accurate RCS at a limited imaging angle to obtain the RCS of the target at any imaging angle. Background Art

[0002] SAR is an active microwave imaging radar that obtains high-resolution SAR images through pulse compression and synthetic aperture. The radar can work around the clock and in all weather conditions, has a certain degree of penetration into vegetation, and has great application value in both military and civilian fields.

[0003] SAR images reflect the backscattering characteristics of the imaged target. The brighter the image, the stronger the target's backscatter. Using a calibrator, we can obtain the conversion coefficient from image grayscale value to backscatter cross-sectional area. Therefore, we can quantitatively calculate the RCS of a specific target under specific imaging conditions (a certain azimuth and angle of incidence) from a SAR image.

[0004] RCS has significant application value. For example, the absolute value of a target's RCS can be used to identify certain targets in SAR images, such as determining the type of ship. By studying the RCS of targets of different materials and angles, we can develop target scattering optimization strategies for studying electromagnetic stealth.

[0005] However, for a variety of reasons, it is difficult to directly obtain RCS at any angle from existing imagery. First, remote sensing image resources are scarce, and the same target cannot be imaged an unlimited number of times, making it impossible to obtain RCS at all imaging angles. Second, the incidence angle of a typical SAR system is between 30 and 60 degrees, making it impossible to obtain RCS at small and large incidence angles. Finally, many targets are parked in fixed positions, such as cars parked in parking spaces with fixed orientations, and ships parked in ports with fixed orientations. This results in only being able to obtain target RCS at a limited azimuth angle. The azimuth angle mentioned above refers to the angle between the ground projection line of the line connecting the radar and the target and the target's head and tail rays, given the satellite's ascending and descending orbit information and left and right view information. The angle of incidence refers to the angle between the radar's incident electromagnetic wave and the target normal. This definition will be used throughout this article.

[0006] In summary, RCS has important applications in target camouflage, electromagnetic stealth, and target detection. However, current RCS acquisition is subject to numerous limitations. This can be summarized as follows: Based on existing images, RCS can only be obtained at certain angles, making it impossible to obtain the RCS of targets at arbitrary azimuths and angles of incidence. Therefore, this patent proposes a method that uses electromagnetic simulation to expand the limited number of RCS values ​​extracted from images, thereby obtaining a more accurate RCS estimate at any imaging angle. Summary of the Invention

[0007] In the case of limited RCS acquisition from images, this paper combines image-domain RCS extraction with electromagnetic simulation RCS, proposing a method for estimating target RCS at all angles based on image extraction and electromagnetic simulation. Addressing the problem of acquiring target RCS at arbitrary imaging angles, this paper constructs a method based on electromagnetic simulation technology to expand the target RCS extracted from images at known imaging angles, thereby accurately estimating the target RCS at any angle.

[0008] A method for estimating the RCS of a target at all angles based on image extraction and electromagnetic simulation includes the following steps:

[0009] Step 1: Prepare the SAR image slice dataset of the research target;

[0010] Step 2: Read the imaging parameters of the target from the auxiliary description file of the original image to which the slice belongs;

[0011] Step 3: Based on the model of the research target, obtain its prior information and combine the orientation, aspect ratio, and peak point detection algorithm to estimate its approximate position and posture in the slice. Based on the target's approximate position and posture, use graphics algorithms and pattern recognition methods to extract its precise outline, and the area within the outline is the target area.

[0012] Step 4: First, convert the original image slice into a backscatter coefficient slice using the quantization factor and calibration constant. Then, use the integration method, combined with the incident angle and image resolution, to perform RCS conversion and accumulation on all pixels in the target area to obtain the true RCS of the target under the current angle conditions.

[0013] Step 5: Using an electromagnetic simulation method based on physical optics and geometric optics, sample the azimuth angle at set intervals within the range of 0 to 360 degrees to obtain a discrete azimuth angle set; sample the incident angle at set intervals within the range of 0 to 90 degrees to obtain a discrete incident angle set; take one azimuth angle and one incident angle at a time, calculate the simulated RCS at that time, and finally form a simulated RCS table with the azimuth angle on the horizontal axis and the incident angle on the vertical axis;

[0014] Step 6: Using the real RCS and the simulated RCS obtained at the corresponding angle, a fitting function is established between the real RCS and the simulated RCS. This fitting function is used to convert the simulated RCS table into a corrected simulated RCS table.

[0015] Step 7: Given any azimuth and incident angle, search the four surrounding corrected simulated RCSs in the corrected simulated RCS table, determine the two adjacent azimuths and two incident angles, and finally use bilinear interpolation to obtain the RCS estimate at the given azimuth and incident angle.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] 1. The present invention combines actual measurement technology with simulation technology, and can use the actual RCS to correct the simulated RCS table. The corrected simulated RCS table can accurately estimate the target RCS at any imaging angle.

[0018] 2. The present invention can automatically extract the target area from the target image slice through the target area automatic extraction algorithm, and automatically calculate the target real RCS using the integration method based on the target area.

[0019] 3. The present invention combines physical optics (PO) and geometric optics (GO) to perform electromagnetic simulation of target echoes. While ensuring sufficient accuracy, the simulation speed is fast enough, which helps to quickly establish a simulated RCS table. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A block diagram of the present invention's all-angle target RCS estimation method based on image extraction and electromagnetic simulation;

[0021] Figure 2 An example target image slice used in the present invention;

[0022] Figure 3 A block diagram of target coarse extraction based on target prior parameters;

[0023] Figure 4 is the minimum bounding rectangle estimation result of a target;

[0024] Figure 5 A box diagram defining the precise target area;

[0025] Figure 6 Defining results for a target area;

[0026] Figure 7 Block diagram for calculating true RCS using the integration method;

[0027] Figure 8 Block diagram for GO+PO method simulation and calculation of RCS;

[0028] Figure 9 It is a three-dimensional scatter plot of simulated RCS, where incidentAngle represents the incident angle and azimuthAngle represents the azimuth angle;

[0029] Figure 10 Figure 3 is a three-dimensional scatter plot of the simulated RCS before and after correction with the real RCS. The circles represent the real RCS and the crosses represent the simulated RCS. DETAILED DESCRIPTION

[0030] The technical solution of the present invention is further described below with reference to the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the scope of protection of the present invention.

[0031] The present invention provides a full-angle target RCS estimation method based on image extraction and electromagnetic simulation. The method uses image domain RCS extraction technology to calculate the target's true RCS from image slices using region definition technology and scattering point integration technology. Based on the principle of electromagnetic scattering on the surface of an object, an electromagnetic calculation method is used. When the imaging angle is the same as that of the image slice, a 3D model of the target is input to obtain the scattering field intensity of the target echo, and then the simulated RCS of the target is calculated. Therefore, the real RCS and simulated RCS at the same imaging angle can be used to establish a conversion function between the actual RCS and the simulated RCS by function fitting. At a certain angle interval, within the entire angle range (azimuth angle of 0 to 360 degrees, incident angle of 0 to 90 degrees), a two-dimensional simulated RCS table is calculated using electromagnetic simulation technology, and then converted into a corrected simulated RCS table using the RCS conversion function. At this time, any imaging angle can be specified, the corresponding position of this angle can be found in the corrected simulated RCS table, and the RCS estimation value at this imaging angle can be obtained using the bilinear interpolation method. The specific steps are as follows:

[0032] Step 1: Prepare a SAR image slice dataset of the target being studied. The number of slices should not be too small, and the azimuth and incident angles should be distributed as evenly as possible across the entire angle range. All target slices should belong to the same target or target of the same model. The specific steps are as follows:

[0033] Step 1: Determine the target model whose RCS you want to study.

[0034] Step 1 and 2: Collect SAR image target slices of the target under the same SAR, different azimuths, and different incident angles. The distribution of azimuth and incident angles should be as uniform and wide as possible, with the azimuth angle range from 0 to 360 degrees and the incident angle range from 0 to 90 degrees.

[0035] Step 13: Form a slice dataset for this target, with the target slice as the data body and the azimuth and incident angle of each slice as labels. It should also include the auxiliary description file of the original SAR image to which the slice belongs.

[0036] Step 2: Read the imaging parameters of the target from the auxiliary description file of the original image to which the slice belongs, which will be used for subsequent image target area definition, RCS electromagnetic simulation, RCS integral calculation, etc. The specific steps are as follows:

[0037] Step 21: Select the appropriate reading function based on the auxiliary description file format. For example, if the auxiliary description information is stored in an XML text file, you can use the XML reading library; if it is stored in a GeoTiff file, you need to use the TIFF reading library to read it.

[0038] Step 22: Based on the product description of the current SAR image, find the tag names corresponding to the imaging parameters required for this step in the current image product auxiliary description file. For example, the tag name corresponding to the target incidence angle is "incidenceAngle", and the tag name corresponding to the ascending and descending orbit information during satellite imaging is "orbit".

[0039] Steps 2 and 3: Use the auxiliary description file reading library to read the target's imaging parameters based on the parameter tag name. These parameters include: image resolution, quantization factor, calibration constant, ascending and descending orbit, left and right view, radar viewing angle, wavelength, bandwidth, radar speed, transmit pulse duration, slant range from the center of the scene, pulse repetition frequency, carrier frequency, range modulation frequency, Doppler center frequency, azimuth sampling rate, number of azimuth sampling points, azimuth sampling duration, range sampling rate, number of range sampling points, and range sampling duration.

[0040] Step 3: Based on the model of the research target, obtain its target size, target surface material, and target reflectivity intensity distribution as prior information. Combined with the orientation, aspect ratio, and peak point detection algorithm, estimate its approximate position and posture in the slice; based on the target's approximate position and posture, use graphics algorithms and pattern recognition methods to extract its precise outline. The area within the outline is the target area. The specific steps are as follows:

[0041] Step 31: Based on the target information, obtain its prior information, including target size, target surface material, and target reflectivity intensity distribution.

[0042] Step 32: Based on the target prior information, eliminate distracting objects that are clearly not the target in the target slice and determine the approximate position and attitude of the target. Position refers to the horizontal and vertical pixel coordinates of the target center in the image slice, and attitude refers to the target's azimuth, which is determined by the target's orientation and the SAR's elevation and elevation trajectory and left-right viewing information.

[0043] Step 3: Calculate multiple feature images based on the target original image, then compress all feature images into a grayscale feature image, and finally perform binary classification on this grayscale feature image. All pixels are judged as 0 or 1, and the set of all pixels with a value of 1 is the target area.

[0044] Step 4: First, convert the original image slice into a backscattering coefficient using a quantization factor and a calibration constant. Then, using the integration method, combined with the incident angle and image resolution, perform RCS conversion and accumulation on all pixels in the target area to obtain the true RCS of the entire target. The specific steps are as follows:

[0045] Step 41: Based on the quantization factor QV and calibration constant K obtained in step 2 dB , converting the original image slice into the backscatter coefficient slice σ0. The specific operation needs to be completed according to the instruction manual given by the specific SAR satellite.

[0046] Step 42: Based on the image resolution read in step 2, obtain the target's resolution Δx and Δy in the x-direction and y-direction, in meters.

[0047] Step 4.3: Using the integration method in SAR image calibration, the target's RCS is expressed as the sum of the product of the pixel area and the backscatter coefficient, as shown in the following formula. This formula is used to extract the true RCS from the image:

[0048]

[0049] Where N is the total number of pixels in the target area, is the i-th pixel of the target area in the backscatter coefficient slice σ0, Δx is the image resolution in the x direction, Δy is the image resolution in the y direction, and RCS target is the true RCS extracted from the image.

[0050] Step 5: Use electromagnetic simulation methods based on physical optics and geometric optics to calculate the simulated RCS for different combinations of azimuth and incident angles, and ultimately form a simulated RCS table with the horizontal axis being the azimuth and the vertical axis being the incident angle. The specific steps are as follows:

[0051] Step 51: Prepare the corresponding 3D model (STL format) according to the research objectives, adjust its physical size and surface scattering parameters, use triangulation to convert it into a set of facets, and save it to a text file. Each facet records the coordinates of the three corner points and the material parameters corresponding to this facet.

[0052] Step 52: Sample the azimuth angle at a set interval within the range of 0 to 360 degrees. This interval should be divisible by 360 to obtain N aA set of azimuth angles, for example, when the sampling interval is 5 degrees, 72 azimuth angles are obtained, namely 0, 5, 10, ..., 350, 355 degrees; the incident angle is sampled at a set interval within 0 to 90 degrees, and this interval should be divisible by 90, so N is obtained. i For example, when the sampling interval is 3 degrees, we get 30 incident angles, 0, 3, 6, ..., 84, 87 degrees; the azimuth angle and the incident angle are combined in pairs, for a total of N a ×N i Various angle combinations, in this N a ×N i Under the imaging conditions of various angle combinations, ray tracing calculations are completed for the 3D model. Then, using physical optics and geometric optics methods, electromagnetic calculations are performed on the ray tracing results to obtain the scattered electric field intensity E of the 3D model under all observation angle combinations. s and the incident electric field strength E i .

[0053] Step 53: Combine the RCS field definition:

[0054]

[0055] E under different imaging angle combinations obtained using electromagnetic calculation S and E i , calculate the simulated RCS under different imaging angle combinations, and finally form a graph with the horizontal axis as azimuth angle, the vertical axis as incident angle, and a total of N a ×N i Simulated RCS table of values.

[0056] Step 6: Based on the real RCS (limited angle) obtained in step 4, find the simulated RCS of the corresponding angle in the simulated RCS table obtained in step 5, establish a fitting function between the real RCS and the simulated RCS, and use this fitting function to convert the simulated RCS table into a corrected simulated RCS table. The specific steps are as follows:

[0057] Step 61: For each target slice, obtain its true RCS i and azimuth a i , angle of incidence b i , and find the target simulated RCS under this angle combination in the simulated RCS table Si .

[0058] Step 62: From step 61, we get the set of all imaging angles {(a1,b1),(a2,b2),...,(a N ,b N )}, the corresponding real RCS set is {RCS1,RCS2,...,RCS N}, the corresponding simulation RCS set is {RCSS1 ,RCS S2 ,...,RCS SN}, input the real RCS and simulated RCS into the fitting function and solve for the fitting function coefficients. The specific form of this fitting function is determined by the number of elements N in the above set, which should be at least 3. In this case, the fitting function takes a second-order polynomial If N is greater than 3, a higher-order polynomial can be selected as the fitting function.

[0059] Step 63: Substitute each value in the simulation RCS table into the fitting function obtained in step 62 to convert the simulation RCS table into a modified simulation RCS table.

[0060] Step 7: Use the corrected simulated RCS table to estimate the target RCS at any angle. Given any azimuth and angle of incidence, look up the four known RCSs around it in the corrected simulated RCS table, determine the two adjacent azimuths and two incident angles, and finally use bilinear interpolation to obtain the RCS estimate at the given azimuth and incident angle. The specific steps are as follows:

[0061] Step 71: Given the imaging azimuth angle a and the incident angle b for obtaining the RCS.

[0062] Step 72: In the modified simulation RCS table, find the RCS of the interval where a and b are located and the four interval vertices. Assume that a is in a i and a i+1 Between, b in b i and b i+1 The four adjacent RCSs of the current angle are {RCS'1, RCS'2, RCS'3, RCS'4}.

[0063] Step 73: Using bilinear interpolation, we can get the estimated value when the azimuth angle is a and the incident angle is b:

[0064]

[0065] Among them, a and b are the imaging azimuth and incident angle corresponding to the current RCS to be estimated, a i and a i+1 is the left and right adjacent azimuth angle of a in the modified simulation RCS table, satisfying a i <a<a i+1 ; b i and b i+1 is the left and right incident angle azimuth of b in the modified simulation RCS table, satisfying b i <b<b i+1 ; RCS'1, RCS'2, RCS'3, RCS'4 are (a i ,b i ),(ai ,b i+1 ),(a i+1 ,b i ),(a i+1 ,b i+1 )Simulation corrected RCS corresponding to the four angle combinations.

[0066] Example:

[0067] This embodiment provides a target RCS estimation method based on image RCS extraction and simulation RCS calculation when the imaging angle is limited, such as Figure 1 As shown, the specific steps include:

[0068] Step 1: Select an ocean transport ship as the research target, collect 50 ocean transport ship image slices and corresponding imaging parameters from the same satellite, with a resolution of 3 meters and a C band. An example is Figure 2 shown.

[0069] The azimuth angles of these target image slices are evenly distributed between 0 and 360 degrees, and the angle of incidence ranges from 28 to 65 degrees (this is the actual angle of incidence range of SAR, while the theoretical range of incidence angles is 0 to 90 degrees). The azimuth angle is the angle between the projection line of the radar-target line and the target's head and tail rays, given the ascending and descending orbit information and the left and right view information. Simply put, it is the target's rotation angle relative to the radar. The angle of incidence is defined as the angle between the radar's incident electromagnetic wave and the target's normal.

[0070] The target slices selected in this embodiment have a sufficiently uniform angular distribution and cover a wide enough angular range to achieve high simulated RCS correction accuracy. Furthermore, the entire set of steps in this embodiment is designed to obtain the RCS of the same target at different angles, so all the slices above correspond to the same target or the same model.

[0071] Step 2: Read the imaging parameters of the target from the auxiliary description file of the image, including image resolution, radar viewing angle, wavelength, bandwidth, radar speed, transmission pulse duration, scene center slant range, pulse repetition frequency, carrier frequency, range modulation frequency, Doppler center frequency, azimuth sampling rate, azimuth sampling points, azimuth sampling duration, range sampling rate, range sampling points, range sampling duration and other information.

[0072] These parameters are mainly divided into two categories. The first category is used for image-based RCS extraction. For example, in order to convert the original image into the backscattering coefficient, a quantization factor is required. The second category is parameters used for electromagnetic simulation, such as electromagnetic wave wavelength, modulation frequency, radar speed, etc. These parameters account for the vast majority of the extracted parameters.

[0073] All parameters are stored in a text file in XML format. By using Python's XML parsing library, the entire file can be read, and then its value string can be obtained by specifying the parameter name. The value string is then converted into the corresponding Python basic type according to the parameter type.

[0074] Step 3: For each target slice, input the target into the target region definition module to obtain the target region. Since the target is a transport ship, we can confirm from research that its aspect ratio is approximately 6. Since the ship lacks a noticeable tower, there are no prominent discrete peaks in the image, and the strong scattering points are relatively evenly distributed. Combining this prior information, we detect the strong scattering regions in the image slices and estimate their azimuth, aspect ratio, peak points, and other information. By comparing this information with the prior information, we estimate the approximate position and posture of the target in the image.

[0075] 1) Target rough extraction based on target prior parameters, the process is as follows Figure 3 shown.

[0076] a) Azimuth parameters

[0077] Due to the sensitivity of SAR images to the target's attitude, the scattering characteristics of targets at different azimuths may be completely different. Different azimuths may lead to differences in the distribution of scattering points and the scattering structure of the target.

[0078] Generally speaking, typical SAR targets are mainly regular-shaped targets, presenting a structure close to a rectangle. Therefore, it performs azimuth fitting of the minimum circumscribed rectangular envelope box. First, the angle of the initial envelope box is selected, the rotation interval is set, and the envelope box is rotated 0° to 180° with the rotation interval as the rotation step, ensuring that the four sides of the envelope box are tangent to the target edge at each angle. Each rotation is calculated according to the rotation criterion. The angle when the optimal envelope coefficient is reached is the azimuth angle of the target. The TBR (Target-to-background ratio) criterion used in this embodiment is:

[0079] Assume that the target rotates n times, and the number of targets in the envelope box during the i-th rotation is N ti , the number of background pixels in the envelope is recorded as N bi , then the envelope coefficient g under TBR can be expressed as:

[0080]

[0081] That is, the angle at which the target-background ratio is the maximum is the target azimuth.

[0082] b) Aspect ratio parameter

[0083] The target's aspect ratio prior information is also important information for target region extraction. When extracting the azimuth angle, the aspect ratio information is introduced to more clearly extract the target's region of interest.

[0084] Generally speaking, the extraction of aspect ratio information can be processed in conjunction with the minimum bounding rectangle. When the ratio of the length to the width of the minimum bounding rectangle does not match the prior information, it is necessary to expand the target area outward. When the ratio is close to the prior information, subsequent operations can be performed directly. Assuming that the length of the minimum bounding rectangle is a and the width is b, the aspect ratio parameter r is expressed as:

[0085]

[0086] For civilian sea freight ships, the aspect ratio can be around 6; for warships, the aspect ratio can even reach 10. In this embodiment, the target is a marine cargo ship, so its prior aspect ratio is set to 6. If the aspect ratio of the minimum bounding rectangle of a target is close to 6, it can be considered that the target is likely to be the target ship. The minimum bounding rectangle estimation result of a ship is as follows: Figure 4 shown.

[0087] c) Peak parameters

[0088] Peak parameter extraction can be used to further determine the accuracy of the target region. In general region extraction, even if the azimuth and aspect ratio parameters are accurately matched, the target region extraction may still produce a certain amount of displacement error. Therefore, peak parameter extraction plays a significant role in accurately locating the target region.

[0089] Peaks typically appear as scattered points, appearing as bright spots in an image. Since only certain areas of a typical volumetric target exhibit bright scattering points, the relative position and scattering intensity of the peak points can be used to estimate the target's shape, size, and some surface properties. In this embodiment, towers and masts on a ship appear as strong scattering points; in addition, some metal objects on the deck also exhibit strong scattering relative to the deck. The distribution of these strong scattering points can be described as follows:

[0090]

[0091] Among them, (x, y) is the position point in the image, x0, y0 respectively represent the horizontal and vertical coordinates of the peak point to be found. are the lengths of the peak point in the two coordinate axis directions, and H1 represents the peak amplitude. Use the quadratic parabola to fit Equation (3):

[0092]

[0093] Among them, five coefficients are represented by peak characteristics:

[0094]

[0095] Since Equation (5) contains five unknown features, at least a 3×3 neighborhood in the SAR image is selected. After solving the coefficients, it is necessary to determine whether there is a maximum value in the neighborhood. The Hessian matrix can be used for this determination. The second-order Hessian matrix can be expressed as:

[0096]

[0097] Then the second-order derivative of H in any β direction can be expressed as:

[0098]

[0099] The eigenvectors of the Hessian matrix are:

[0100]

[0101] By the Rayleigh-Ritz inequality:

[0102] λ min ||x||≤x'Hx≤λ max ||x|| (9)

[0103] Among them, λ min and λ max is the eigenvalue of the H matrix, so:

[0104] λ min ||x||≤I' β (x,y)≤λ max ||x|| (10)

[0105] It can be determined that if λ min ,λ max are all less than 0, then I" β When (x,y) is less than 0, it is a peak point. Therefore, the peak pixel points corresponding to the target can be obtained. Based on the coordinate distribution of these peak pixel points, the approximate position and posture of the target can be determined.

[0106] After obtaining the approximate position and posture of the target through the above-mentioned prior estimation information, it is necessary to further extract the fine contour and area of ​​the target. The process is as follows Figure 5 shown.

[0107] 2) Accurate region extraction based on graphics algorithms and pattern recognition algorithms

[0108] Various texture features of SAR images can be captured using the gray-level co-occurrence matrix (GLCM), a method for describing texture using spatial correlation. GLCM calculates the frequency of occurrence of structures composed of pixels at multiple gray levels within an image. This gray-level structure can reflect changes in the image's grayscale. The gray-level co-occurrence matrix can be used to obtain comprehensive information about the image's grayscale under various parameters, such as movement direction, movement step size, and grayscale amplitude difference.

[0109] The gray-level co-occurrence matrix itself can partially reflect the gray-level texture information in the image. However, based on the gray-level co-occurrence matrix, using several formulas, more statistical feature matrices reflecting various image information can be calculated, such as mean, variance, entropy, etc.

[0110] To obtain a binary representation of target and non-target areas using statistical features, we first use the PCA algorithm to perform principal component analysis on all features. Then, we select the top three principal components and convert them to the HSI domain. HSI is a color model that converts RGB colors into a cylindrical space for representation, where I represents intensity. In the I component, the contrast between target and non-target areas is very strong, facilitating binarization. The reason for using brightness threshold segmentation to extract building areas in SAR images is that the average grayscale of building areas in SAR images is high, and the resulting texture feature component also has a high average grayscale for building areas. The brightness component in the HSI model precisely highlights the high grayscale characteristics of the original SAR image.

[0111] After obtaining the I component, we then use the adaptive binary segmentation algorithm to obtain a grayscale threshold based on the grayscale distribution of the I component. All pixels in I with grayscale values ​​above this threshold are considered target pixels, and their grayscale values ​​are set to 1. All other pixels are considered non-target pixels, and their grayscale values ​​are set to 0. At this point, all areas with grayscale values ​​of 1 are target areas. An example of target area extraction is shown in the figure below. Figure 6 shown.

[0112] Step 4: First convert the original image into a backscattering coefficient image, and then use the integral method to calculate the RCS. The whole process is as follows: Figure 7 shown.

[0113] The original grayscale value of the SAR image reflects the digital value of the radar echo signal after sampling and quantization. The relative size of the pixel grayscale can reflect the relative intensity of the backscatter of electromagnetic waves by different ground objects. However, if you want to get the absolute value of the backscatter intensity, you need to calibrate the SAR image first, that is, convert the digital value (DN) into the backscatter coefficient.

[0114] The DN value has been converted into the backscattering coefficient in step 2. Quantization factor QV (QualifuValue) and calibration constant K dB (CarlibConst).

[0115]

[0116] Here, n represents the number of bits of a pixel, and generally n=16.

[0117] After obtaining the backscatter coefficient, the RCS is extracted from the image using the integration method, combined with the target area definition results and the scattering mechanism of the SAR image.

[0118] When an object is irradiated by electromagnetic waves, energy is scattered in all directions. The sum of the scattered field and the incident field constitutes the total field in space. The spatial distribution of the scattered energy depends on properties such as the object's shape, size, and structure, as well as the frequency of the incident wave. This energy distribution is called scattering and is characterized by the scattering cross section, which is a hypothetical area of ​​the object. The object itself is often called a target or scatterer.

[0119] Generally speaking, for image data, the backscatter coefficient of the target can be calculated by the RCS of the target and the physical size of the target:

[0120]

[0121] The total target area is:

[0122] S target =Δx×Δy×N (13)

[0123] Where Δx and Δy are the resolutions of the target in the x-direction and y-direction respectively, and N is the total number of pixels of the target.

[0124] Then we can use the idea of ​​differentiation to decompose the RCS of the target into the sum of the products of pixel points and backscatter coefficients. This is the integration method, as shown in the following formula:

[0125]

[0126] After calculation, the average RCS value of all slices is 46.33dB.

[0127] Step 5: Combine the physical optics method and the geometric optics method to achieve rapid RCS simulation calculation of ship targets while ensuring the accuracy of RCS calculation.

[0128] Physical optics (PO) is a typical high-frequency approximation method that represents the scattered field as the integral of the induced current on the scatterer's surface. The induced surface current of the scatterer is determined using a geometric optics approximation. PO is commonly used to address electromagnetic scattering problems from electrically large metallic targets. Therefore, in this example, PO is used to calculate the odd-order scattered field of a target surface element.

[0129] The scattered field formula under the physical optics method can be derived from the basic Stratton-Chu integral equation. The Stratton-Chu integral equation is an equation that automatically satisfies boundary conditions and radiation conditions. That is, in a passive space, the electromagnetic field can be expressed as an integral on a closed surface, that is:

[0130]

[0131] in, is the unit normal vector at a point r′ on the surface, ω is the frequency, μ and ε are the magnetic permeability and dielectric constant of the medium respectively, E T 、H T are the total fields at r′, and ψ0 is the Green’s function of free space, namely:

[0132]

[0133] Given the assumption that the dark-sector current is zero, the surface is divided into an illuminated region S1 and a shadowed region S2, separated by a line called the shadow boundary Γ. The shadow boundary Γ represents a discontinuity, so the continuity condition required to derive the integral equation using Green's theorem cannot be met. This discontinuity can be overcome by adding a line integral term along Γ, namely:

[0134]

[0135] Among them, ε0 and μ0 are the vacuum dielectric constant and vacuum permeability respectively, are the scattered fields at point P. In the far field, the far-field electric field of the target derived by the physical optics method is:

[0136]

[0137] PO calculates the scattered field based on the basic idea of ​​Geometric Optics (GO). That is, after the incident wave is incident on the object, the reflected field is calculated according to the Fresnel formula. Then, according to the equivalence principle, the incident field and the reflected field are equivalent to electromagnetic currents. The specific basis of the equivalence is the boundary conditions of the electromagnetic field.

[0138] Specifically, the surface element scattering field that undergoes multiple scattering is calculated using the geometric optics method combined with PO, and the reflection field before the last scattering is calculated using GO. GO is very suitable for the calculation of multiple refractions and reflections. In the process of radar emitting electromagnetic waves and multiple scattering, the generated reflection fields and coupling fields can be calculated using GO. Geometric optics was originally used to analyze the propagation of extremely high-frequency electromagnetic waves. This method treats electromagnetic waves as propagating through electromagnetic ray tubes, and can be used to approximate the direct radiation, reflection, and refraction problems during the propagation of electromagnetic waves. Since the fluctuation of electromagnetic waves is no longer obvious under extremely high frequency conditions, the propagation of electromagnetic wave energy can be explained by the intensity law of geometric optics. This expression indicates that the total energy along a ray tube is a constant.

[0139] |E1| 2 ·dS1=|E2| 2 ·dS2 (21)

[0140] The intensity law of geometric optics can be used to determine the change of field intensity along the direction of the ray. Applying it to the ray tube can obtain the expression for the propagation of the electric field in a uniform medium, namely:

[0141]

[0142] Where exp(-jkr) is the spatial phase delay and r is the length of the ray path. Similarly, applying the geometric optics intensity law to inhomogeneous media, we can obtain the expressions for the reflected and refracted fields, namely:

[0143]

[0144] Among them, R hv and T h / v are the reflection coefficient and transmission coefficient respectively, dS1, dS2 and dS3 represent the cross-sectional areas of the incident ray tube, the reflected ray tube and the transmitted ray tube respectively, r1, r2 and r3 represent the path lengths of the incident ray tube, the reflected ray tube and the refracted ray tube respectively.

[0145] From this we can conclude that the reflection coefficient calculated by GO is:

[0146]

[0147] Where R is the Fresnel reflection coefficient. Combining the reflection coefficient and the odd scattered field calculated by PO, the target's multiple scattered electric field E or magnetic field H can be obtained. The above calculation process is as follows: Figure 8 shown.

[0148] Radar cross section (RCS) is a measure of the returned or scattered power in a given direction based on the concept of isotropic scattering by a target under plane wave illumination. It is normalized by the power density of the incident field. Formally, the definition of radar cross section is:

[0149]

[0150] Where P scat and P inc It represents the energy flux density of the scattered wave at the radar receiver and the incident wave at the target; E s and E i represents the scattered electric field at the radar receiver and the incident electric field at the target; H s and H i represents the scattered magnetic field at the radar receiver and the incident magnetic field at the target.

[0151] As we all know, the scattered field is caused by the presence of scatterers (targets) in space, so the total field in space is the sum of the incident field and the scattered field, that is:

[0152] E=E i +E s (27)

[0153] H=H i +H s (28)

[0154] From Equation (26), we can see that RCS is a limit, which is obtained when the distance R tends to infinity. However, since the incident wave is assumed to be a plane wave, P inc 、E i and H i are all constants, P scat Proportional to 1 / R in far field conditions 2 , E s and H s In far-field conditions, it is proportional to 1 / R. In actual calculations, it is sufficient to simply set R so that the radar receiver is located in the far region of target scattering. Equation (26) also shows that RCS is 4π times the ratio of the power density scattered by the target in the receiving direction to the power density incident on the target from a given direction within a unit solid angle.

[0155] As mentioned earlier, RCS is a measure of an object's ability to scatter electromagnetic waves and is a hypothetical area of ​​the object. From the above definition, it is clear that the electromagnetic energy scattered by a radar target in a given direction can be expressed as the product of the target's RCS and the incident power density. In fact, the energy flux density of the incident plane wave is:

[0156]

[0157] Where Y0 is the free space admittance. Based on the concept of effective area of ​​antenna aperture, the total power intercepted by the target is the product of the incident power density and the target equivalent area (RCS) σ, that is:

[0158]

[0159] Assuming that the power is scattered isotropically in all four solid angles, the scattered wave energy flux density at a distance R from the target is:

[0160]

[0161] The scattered wave energy flux density can be expressed as the scattered field intensity E s To express, that is:

[0162]

[0163] From equations (31) and (32), we can get:

[0164]

[0165] In formula (33), when the distance R is far enough, the incident wave irradiating the target is approximately a plane wave, and σ is independent of R. This is equivalent to formula (26).

[0166] In fact, the RCS of a target may be very large, as large as tens of thousands of square meters, or very small, as small as a few square centimeters. The range of variation is too large to be conveniently expressed, so it is often expressed in logarithmic form. The conversion relationship between the two is:

[0167]

[0168] RCS is a function of the following factors: target structure; frequency of the electromagnetic wave; polarization of the incident field; polarization of the received electric field; and angular position of the target relative to the direction of the incoming wave.

[0169] The basic RCS expression can be used to obtain the radar cross section of a target in a certain direction:

[0170]

[0171] Among them, P inc is the power density of the incident wave. The RCS expression shows that the radar cross section is a function of θ and φ. Therefore, by adjusting θ and φ, the RCS of a target under different azimuth and angle of incidence conditions can be obtained. Furthermore, by adjusting the incident wave frequency to cover the L and X bands, the RCS of a target at each frequency can be easily determined.

[0172] The above is a method for calculating the RCS of a target under azimuth and incident angle. Furthermore, in this embodiment, the azimuth angle ranges from 0 to 360 degrees, with a point taken every 10 degrees, for a total of 36 azimuth angles; the incident angle ranges from 0 to 90 degrees, with a point taken every 5 degrees, for a total of 18 incident angles; the combination of incident angle and azimuth angle provides a total of 648 imaging angle conditions. The above RCS simulation algorithm is used to calculate these 648 conditions, obtaining a simulated RCS table with 648 elements, which is plotted in three-dimensional space as scattered points, as shown in the following figure: Figure 9 As shown in the figure, the average RCS value is calculated to be 43.57dB.

[0173] Step 6: Assume that the imaging condition set corresponding to all image slices is {(a1,b1),(a2,b2),...,(a N ,b N )}, where a is the azimuth angle and b is the incident angle. The corresponding set of real RCS extracted from the target slice is {RCS1,RCS2,...,RCS N}, the simulated RCS corresponding to the same imaging angle is {RCS S1 ,RCS S2 ,...,RCS SN}, input the pairs of real RCS and simulated RCS into the polynomial fitting function:

[0174]

[0175] The order of the fitting function is 2, and the polynomial coefficients are obtained by solving it. This polynomial can be used to convert the simulated RCS table into a corrected simulated RCS table. Although this table is not equivalent to the true RCS table, its mean square error with the true RCS table is the smallest, and it can be used to predict the RCS of unknown imaging angles relatively accurately within an acceptable error. The RCS scatter plots before and after correction are shown in the figure below. Figure 10 As shown in the figure, it can be seen that the corrected simulated RCS is generally close to the true RCS value, and the trend of change with angle is also similar, which shows that the correction effect of the true RCS on the simulated RCS is good.

[0176] The average RCS of the corrected simulated RCS table is 46.15dB, and the mean square error compared with the true RCS is 0.27dB.

[0177] Step 7: Arbitrarily specify the unknown imaging azimuth and incident angle, input them into the electromagnetic simulation model, obtain the target simulation image, and calculate the simulated RCS; input the simulated RCS into the fitting function to obtain the RCS estimate closest to the true value.

[0178] Assume that you want to get the RCS of the target when the azimuth is a and the incident angle is b, change the azimuth in the simulation parameters to a and the incident angle to b, where a is i and a i+1 Between, b in b i and b i+1 Between. Checking the modified simulation RCS table in step 6, we can get i ,b i ),(a i ,b i+1 ),(a i+1 ,b i ),(a i+1 ,b i+1 Correction simulation under four imaging angles Abbreviated as {RCS'1,RCS'2,RCS'3,RCS'4}.

[0179] Using bilinear interpolation, we can get the estimated RCS value when the azimuth angle is a and the incident angle is b.

[0180]

[0181] For example, when the azimuth angle is 43 degrees, it is between 40 and 50 degrees; when the incident angle is 72 degrees, it is between 70 and 75 degrees. Looking up the table, when the azimuth angle is 40 degrees and the incident angle is 70 degrees, the RCS is 46.55 dB. Similarly, the other three adjacent RCS values ​​are 46.46 dB, 46.41 dB, and 46.78 dB. Using formula (37), we can calculate that when the azimuth angle is 43 degrees and the incident angle is 72 degrees, the estimated RCS value of the target is 46.52 dB.

Claims

1. A full-angle target RCS estimation method based on image extraction and electromagnetic simulation, characterized by The method comprises the following steps: Step 1: Prepare the SAR image slice dataset of the research target; Step 2: Read the imaging parameters of the target from the auxiliary description file of the original image to which the slice belongs; Step 3: Based on the model of the research target, obtain its prior information and combine the orientation, aspect ratio, and peak point detection algorithm to estimate its approximate position and posture in the slice. Based on the target's approximate position and posture, use graphics algorithms and pattern recognition methods to extract its precise outline, and the area within the outline is the target area. Step 4: First, convert the original image slice into a backscatter coefficient slice using the quantization factor and calibration constant. Then, use the integration method, combined with the incident angle and image resolution, to perform RCS conversion and accumulation on all pixels in the target area to obtain the true RCS of the target under the current angle conditions. Step 5: Using an electromagnetic simulation method based on physical optics and geometric optics, sample the azimuth angle at set intervals within the range of 0 to 360 degrees to obtain a discrete azimuth angle set; sample the incident angle at set intervals within the range of 0 to 90 degrees to obtain a discrete incident angle set; take one azimuth angle and one incident angle at a time, calculate the simulated RCS at that time, and finally form a simulated RCS table with the azimuth angle on the horizontal axis and the incident angle on the vertical axis; Step 6: Use the real RCS and the simulated RCS obtained at the corresponding angle to establish a fitting function between the real RCS and the simulated RCS. Use this fitting function to convert the simulated RCS table into a corrected simulated RCS table. The specific steps are as follows: Step 61: For each target slice, obtain its true and azimuth , angle of incidence , and find the target simulation under this angle combination in the simulation RCS table ; Step 62: The set of all imaging angles obtained from step 61 is , the corresponding real RCS set is , the corresponding simulation RCS set is , input the real RCS and simulated RCS into the fitting function and solve for the fitting function coefficients; Step 63: Substitute each value in the simulation RCS table into the fitting function obtained in step 62 to convert the simulation RCS table into a modified simulation RCS table; Step 7: Given any azimuth and incident angle, search the four surrounding corrected simulated RCSs in the corrected simulated RCS table, determine the two adjacent azimuths and two incident angles, and finally use bilinear interpolation to obtain the RCS estimate for the given azimuth and incident angle. The specific steps are as follows: Step 71: Given the imaging azimuth angle at which you want to obtain RCS and the angle of incidence ; Step 72: In the corrected simulation RCS table, search and The RCS of the interval and the four interval vertices, assuming exist and between, exist and The four adjacent RCSs of the current angle are ; Step 73: Use bilinear interpolation to get the azimuth angle , the incident angle is Estimated value at: in, and is the imaging azimuth and incident angle corresponding to the RCS to be estimated currently, and for The left and right adjacent azimuths in the corrected simulation RCS table meet the requirements. ; and for The left and right incident angles in the corrected simulation RCS table satisfy ; They are Simulation corrected RCS corresponding to the four angle combinations.

2. The all-angle target RCS estimation method based on image extraction and electromagnetic simulation according to claim 1 is characterized in that The specific steps of step one are as follows: Step 1: Determine the target model whose RCS is to be studied; Step 1 and 2: Collect SAR image target slices of the target under the same SAR, different azimuths, and different incident angles, where the azimuth angle range is 0 to 360 degrees and the incident angle range is 0 to 90 degrees; Step 13: Form a slice dataset for this target, with the target slice as the data body and the azimuth and incident angle of each slice as labels. It should also include the auxiliary description file of the original SAR image to which the slice belongs.

3. The method for estimating the RCS of a target at all angles based on image extraction and electromagnetic simulation according to claim 1 is characterized in that The specific steps of step 2 are as follows: Step 21: Select the appropriate reading function according to the auxiliary description file format; Step 22: According to the product description of the current SAR image, find the corresponding label name of the imaging parameters required in this step in the auxiliary description file of the current image product; Step 2 and 3: Use the auxiliary description file reading library to read the imaging parameters of the target according to the parameter label name.

4. The method for estimating the RCS of a target at all angles based on image extraction and electromagnetic simulation according to claim 3 is characterized in that The imaging parameters specifically include: image resolution, quantization factor, calibration constant, ascending and descending orbit, left and right view, radar downward viewing angle, wavelength, bandwidth, radar speed, transmission pulse duration, scene center slant range, pulse repetition frequency, carrier frequency, range frequency modulation, Doppler center frequency, azimuth sampling rate, azimuth sampling points, azimuth sampling duration, range sampling rate, range sampling points, and range sampling duration.

5. The method for estimating the RCS of a target at all angles based on image extraction and electromagnetic simulation according to claim 1 is characterized in that The specific steps of step three are as follows: Step 31: Based on the target information, obtain its prior information, including target size, target surface material, and target reflectivity intensity distribution; Step 32: Based on the target prior information, eliminate interference objects that are obviously not the target in the target slice and determine the approximate position and attitude of the target. The position refers to the horizontal and vertical pixel coordinates of the target center in the image slice, and the attitude refers to the azimuth of the target, which is determined by the target placement direction and the SAR's elevation and elevation trajectory and left and right view information. Step 3: Calculate multiple feature images based on the target original image, then compress all feature images into a grayscale feature image, and finally perform binary classification on this grayscale feature image. All pixels are judged as 0 or 1, and the set of all pixels with a value of 1 is the target area.

6. The method for estimating the RCS of a target at all angles based on image extraction and electromagnetic simulation according to claim 1 is characterized in that The specific steps of step 4 are as follows: Step 41: Based on the quantization factor obtained in step 2 and the calibration constant , converting the original image slices into backscattering coefficient slices ; Step 42: According to the image resolution read in step 2, obtain the target Direction and Resolution in direction and ; Step 4.3: Using the integration method in SAR image calibration, the target's RCS is expressed as the sum of the product of the pixel area and the backscatter coefficient, as shown in the following formula. This formula is used to extract the true RCS from the image: Where, is the total number of pixels in the target area, is the backscatter coefficient slice The i-th pixel of the target area in is the image resolution in the x direction, is the image resolution in the y direction, is the true RCS extracted from the image.

7. The method for estimating the RCS of a target at all angles based on image extraction and electromagnetic simulation according to claim 1 is characterized in that The specific steps of step five are as follows: Step 51: Prepare the corresponding 3D model according to the research objectives, adjust its physical dimensions and surface scattering parameters, convert it into a set of facets using triangulation, and save it to a text file. Each facet records the coordinates of the three corner points and the material parameters corresponding to the facet. Step 52: Sample the azimuth angle at a set interval within the range of 0 to 360 degrees. This interval should be divisible by 360. The incident angle is sampled at a set interval between 0 and 90 degrees, and this interval should be divisible by 90, so The set of incident angles; the combination of azimuth and incident angles is A combination of angles, here Under the imaging conditions of various angle combinations, ray tracing calculations are completed for the 3D model. Then, using physical optics and geometric optics methods, electromagnetic calculations are performed on the ray tracing results to obtain the scattered electric field intensity of the 3D model under all observation angle combinations. and the incident electric field strength ; Step 53: Combine the RCS field definition: The different imaging angle combinations obtained by electromagnetic calculation and , calculate the simulated RCS under different imaging angle combinations, and finally form a graph with the horizontal axis as azimuth, the vertical axis as incident angle, and a total of Simulated RCS table of values.

Images