CN110109099B - Earth surface orientation angle estimation method and system based on scattering similarity entropy self-adaptive expansion - Google Patents
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Abstract
The invention provides a surface orientation angle estimation method based on scattering similarity entropy self-adaptive expansion, which comprises the following steps: obtaining a coherent matrix of the earth surface according to polarization data of the fully-polarized SAR; calculating a Huynen parameter according to the coherent matrix; calculating scattering similarity entropy parameters according to the Huynen parameters; distinguishing earth surface states including earth surface vegetation areas and earth surface bare areas based on the scattering similarity entropy parameters; calculating orientation angle estimation without a specific reference axis and expanded orientation angle estimation; and obtaining the earth surface orientation angle estimation according to the earth surface state by combining the orientation angle estimation without the specific reference axis and the expanded orientation angle estimation. The invention further provides a surface orientation angle estimation system based on scattering similarity entropy self-adaptive expansion. The method and the system avoid the problems of angle winding and inaccurate estimation caused by over-small estimation range of the traditional algorithm; the problem that the noise of the result obtained when the expanded orientation angle estimation method is applied to the vegetation area is too high is solved, and more accurate estimation of the earth surface orientation angle can be obtained.
Description
Technical Field
The invention relates to the field of polarization orientation angle estimation of a fully-polarized synthetic aperture radar target, in particular to a surface orientation angle estimation method based on scattering similarity entropy self-adaptive expansion, and the method is particularly suitable for estimating the polarization orientation angle of a surface target according to the condition that the surface is covered or not.
Background
With the development of microwave technology, a Synthetic Aperture Radar (SAR for short) is widely applied to the aspects of target detection and identification, ground object classification, surface parameter inversion and the like as one of important means of microwave remote sensing. The polarization orientation angle of the target refers to the angle of rotation of the target about the radar line of sight. As an important parameter of the fully polarized radar data, the method has an indispensable meaning for target property description and orientation analysis. The specific relationship between the polarization orientation angle and the surface gradient undulation makes it of interest as an important parameter for terrain inversion, as in document 1[ J.S.Lee, D.L.Schuler, and T.L.Ainsworth, "polar SAR data composition for terrain azimuth slope variation," IEEE trans.Geosci.Remote Sens.,2000,38(5): 2153-.
Circular polarization algorithm is one of the most widely used terrain orientation angle estimation algorithms currently in use, such as document 2[ j.s.lee, d.l.schuler, t.l.air, e.g., krogager, d.kasilingam, and w. -m.boerner, "On the estimation of the radius orientation shift induced by gradient coils," IEEE trans.geosci.remote sensors, 2002,40(1):30-41], and the obtained result of the terrain orientation angle has high consistency with the actual measurement data. However, since the circular polarization algorithm limits the solution range of the target orientation angle to between [ -45 °,45 ° ] rather than the range of [ -90 °,90 ° ] of the actual terrain orientation, it will cause errors in estimating the orientation angle of steep terrain. Aiming at the problem, an expanded steep terrain orientation angle estimation method is provided, a reference axis of an angle is determined by combining with a target scattering characteristic, and the expanded orientation angle estimation method expands a winding orientation angle, so that accurate estimation of the steep terrain orientation angle is obtained.
Although the expanded estimation algorithm for the orientation angle of the steep terrain solves the estimation problem of the large orientation angle of the steep terrain, the terrain condition can be reflected more accurately. However, in the vegetation area, the extended orientation angle estimation result has higher noise. The scattering of the vegetation area shows high randomness, so that the selection of an angle reference axis is influenced, and the expansion has certain randomness. Since the vegetation area does not conform to the scattering model of the earth's surface, it makes no sense to choose the reference axis. More essentially, due to the coverage of the vegetation on the ground surface, the radar echo is difficult to truly reflect the orientation condition of the ground surface, and the extension of the orientation angle of the vegetation area has no significance. The same expanding operation of the vegetation area and the orientation angle of the common earth surface is not necessary in the expanded steep terrain orientation angle estimation method, and the error of the orientation angle estimation result is increased.
The scattering similarity entropy parameter is a parameter proposed by Li and Zhang to describe randomness of scattering of a target, such as document 3[ d.li and y.zhang, "Random similarity-based entropy/alpha classification of polarisar data," IEEE j.sel.topics appl.earth observer.remote sens, 2017, 10 (12): 5712-5723]. Both theoretical derivations and experimental results indicate that the scattering-like entropy parameter has the same physical meaning as the polarization entropy, as described in document 4[ s.r. cloud and e.pottier, "An entry based classification scheme for land applications of polar experimental SAR," IEEE trans. geosci. remote sens, 1997, 35 (1): 68-78] and, in contrast to polarization entropy, Hs has the advantage of being computationally simple and of not requiring feature decomposition.
Disclosure of Invention
The invention aims to solve the problem that the estimation result obtained by the method for estimating the orientation angle of the earth surface with a large orientation angle in the vegetation area has high error.
The vegetation area has higher scattering randomness, so the vegetation area has higher scattering similarity entropy Hs value. The scattering similarity entropy parameter Hs is a parameter which describes scattering randomness and is irrelevant to the orientation of the target, and can reflect the scattering type of the target to a certain degree; according to the scattering similarity entropy Hs of the target, the vegetation area and the bare land area can be effectively distinguished.
According to the method, the vegetation area and the bare earth surface area are distinguished, and the expanded target orientation angle estimation is selected in a self-adaptive manner, so that the problem that the expanded orientation angle estimation method has a large error in the vegetation area is solved, and the accurate earth surface orientation angle estimation method which can expand the earth surface orientation angle estimation range and reduce the noise influence of the vegetation area is obtained.
In order to achieve the above object, the present invention provides a surface orientation angle estimation method based on scattering similarity entropy adaptive expansion, including:
step 1) obtaining a coherent matrix [ T ] of a target according to polarization data of the full-polarization synthetic aperture radar]Coherent matrix of objects [ T ]]Is an Hermite matrix, and calculates Huynen parameter A0,B0B, C, D, E, F, G and H;
step 2) obtaining the Huynen parameter A according to the step 1)0,B0B, C, D, E, F, G and H, and calculating a target scattering similarity entropy parameter Hs;
step 3) self-adaptive expansion selection of orientation angle estimation is carried out based on the scattering similarity entropy parameter Hs obtained in the step 2):
if Hs is not less than 0.31345, based on HuyThe nen parameters B and E adopt the traditional estimation method to calculate the orientation angle without specific reference axis
Otherwise, if Hs is less than 0.31345, calculating an expanded orientation angle by adopting an expanded orientation angle estimation method based on the Huynen parameters B, E, C and H
Step 4) obtaining the final self-adaptive expanded earth surface orientation angle estimation by using the result of the step 3)
In the above technical solution, the step 1) specifically includes: obtaining a coherent matrix [ T ] of the target according to the polarization data of the full-polarization synthetic aperture radar]Calculating the Huynen parameter A0,B0B, C, D, E, F, G and H; wherein the content of the first and second substances,
the coherence matrix [ T ] of the target is represented as follows:
huynen parameter A0,B0The calculation formulas for B, C, D, E, F, G and H are as follows:
C=Re{T12}
D=-Im{T12}
E=Re{T23}
F=Im{T23}
G=Im{T13}
H=Re{T13}
wherein Re {. is a real part, and Im {. is an imaginary part.
As an improvement of the method, the calculation formula of the scattering similarity entropy Hs in step 2) is:
hs belongs to [0,1], Hs is convenient to calculate, and feature decomposition or other complex operations are not needed, so that the calculation cost is effectively reduced.
As an improvement of the method, in the step 3), adaptive expansion selection of the orientation angle estimation is performed based on the scattering similarity entropy parameter Hs: if Hs is more than or equal to 0.31345, calculating the orientation angle without the specific reference axis by using Huynen parameters B and E and adopting a traditional estimation methodWherein the content of the first and second substances,
calculation of orientation angles without specific reference axes using conventional methodsComprises the following steps:
if Hs <0.31345, then based on Huynen parameter C, H and orientation angle without specific reference axisCalculating an adaptive expansion selection parameter C':
c' selects parameters for expansion:
based on Huynen parameters B, E, C and H, expanding the angle between the orientation angle estimation method and the vertical polarization axis v, namely expanding the orientation angle estimation
Wherein the content of the first and second substances,is the result obtained by using the conventional orientation angle estimation method;
using the results of step 3), combiningAndobtaining a final adaptively extended surface orientation angle estimateThe formula is as follows:
the invention also provides a surface orientation angle estimation system based on scattering similarity entropy self-adaptive expansion, which comprises the following components: the device comprises a coherent matrix acquisition module, a parameter calculation module, a scattering similarity entropy calculation module, a ground surface state distinguishing module and a ground surface orientation angle estimation module;
the coherent matrix acquisition module is used for acquiring a coherent matrix of a target according to polarization data of the full-polarization synthetic aperture radar;
the parameter calculation module is used for calculating a Huynen parameter according to the coherent matrix;
the scattering similar entropy calculation module is used for solving a scattering similar entropy parameter Hs according to the Huynen parameter;
the earth surface state distinguishing module is used for distinguishing earth surface states by scattering similar entropy parameters, and the earth surface states comprise earth surface vegetation areas and earth surface exposed areas;
the earth surface orientation angle estimation module is used for carrying out traditional orientation angle estimation or expanded orientation angle estimation on the earth surface orientation angle according to the earth surface state to obtain accurate earth surface orientation angle estimation.
The invention also provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor implements the method when executing the computer program.
The invention also proposes a computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, causes the processor to carry out the above-mentioned method.
The invention has the advantages that:
the earth surface orientation angle estimation method based on scattering similarity entropy self-adaptive expansion not only expands the estimation range of the orientation angle, but also avoids the problems of angle winding, inaccurate estimation and the like caused by the over-small estimation range of the traditional algorithm; and the problem that the noise of the result obtained by applying the expanded orientation angle estimation method to the vegetation area is too high is solved, and a more accurate orientation angle estimation result can be obtained.
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FIG. 1 is a flow chart of a method for estimating a surface orientation angle based on scattering similarity entropy adaptive expansion according to the present invention;
FIG. 2 is a schematic diagram of a fully-polarized synthetic aperture radar image used in an embodiment of the earth surface orientation angle estimation method based on scattering similarity entropy adaptive expansion according to the present invention;
FIG. 3 shows the polarization orientation angle results calculated using DEM data;
FIG. 4 is an orientation angle result using an expanded orientation angle estimation method;
FIG. 5 is a scattering similarity entropy result of polarization data of an embodiment of a surface orientation angle estimation method based on scattering similarity entropy adaptive expansion of the present invention;
FIG. 6 shows the estimation result of the earth surface orientation angle obtained by the earth surface orientation angle estimation method based on scattering similarity entropy adaptive expansion of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
As shown in fig. 1, the method for estimating the earth surface orientation angle based on scattering similarity entropy adaptive expansion of the invention includes the following steps:
step 1) obtaining a coherent matrix [ T ] of a target according to polarization data of the full-polarization synthetic aperture radar]Calculating the Huynen parameter A0,B0B, C, D, E, F, G and H;
step 2) obtaining the Huynen parameter A according to the step 1)0,B0B, C, D, E, F, G and H, and calculating a target scattering similarity entropy parameter Hs;
step 3) self-adaptive expansion selection of orientation angle estimation is carried out based on the scattering similarity entropy parameter Hs obtained in the step 2): if Hs is more than or equal to 0.31345, estimating the orientation angle without specific reference axis by using Huynen parameters B and E by adopting a traditional estimation method
Otherwise, if Hs is less than 0.31345, calculating the orientation angle estimation of the target expansion by adopting an expanded orientation angle estimation method based on the Huynen parameters B, E, C and H
Step 4), obtaining the final self-adaptive expanded earth surface orientation angle estimation according to the step 3)
This is further described below by way of example.
In step 1), a coherent matrix [ T ] of the target is obtained according to polarization data of the full-polarization synthetic aperture radar]The coherence matrix [ T ] of the object]Is an Hermite matrix, and calculates Huynen parameter A0,B0B, C, D, E, F, G and H; wherein the content of the first and second substances,
the coherence matrix [ T ] of the target is represented as follows:
huynen parameter A0,B0The calculation formulas for B, C, D, E, F, G and H are as follows:
wherein, the Huynen parameter A0,B0B, C, D, E, F, G and H are all real numbers. The coherence matrix [ T ] of the object]The adoption of real number parametric representation has clear advantages. The expression of the orientation angle by using the Huynen parameter has the advantages of simplicity and intuition. The two representations are equivalent.
In one embodiment, the full-polarization synthetic aperture radar data used is shown in FIG. 2, which is a regional observation of Camp Roberts, Calif., USA acquired by the airborne AIRSAR System of NASA/JPL in 1998. The region of the areaThe shape fluctuation is obvious, and the vegetation is distributed in the valleys. Since the AIRSAR obtains terrain elevation (DEM) data by using the C-band interferometric synthetic aperture radar in the area, the orientation angle of the earth surface can be calculated by combining the DEM and the radar incidence angle informationThe relationship between orientation angle and terrain slope is as follows:
where ω is the surface azimuth inclination, γ is the surface range inclination, and φ is the radar wave incidence angle. The results of the orientation angle calculated by equation (3) are shown in fig. 3.
The formula (3) can be used for deducing that the value range of the earth surface orientation angle is between [ -90 degrees and 90 degrees ], but the traditional orientation angle estimation algorithm, such as a circular polarization algorithm, can only calculate the orientation angle within [ -45 degrees and 45 degrees ], which indicates that the angle beyond the range generates a winding phenomenon, and the estimation result is inaccurate. The expanded orientation angle estimation method combines a surface Bragg scattering model to define a reference axis of an orientation angle, so that an angle range is expanded, and an orientation angle estimation result within [ -90 degrees, 90 degrees ] can be obtained, and the result in the embodiment is shown in fig. 4. Comparing the results obtained from DEM, it can be seen that the results obtained from the expanding method approximately match the actual results of fig. 3, but that the noise is higher in some regions, especially for the covered regions. And in these regions the orientation angle is very large, approaching ± 90 °. This shows that the algorithm does not have good results for the spread of the orientation angle of the vegetation coverage area. This is reasonable. Because the propagation algorithm is established based on a surface Bragg scattering model, the vegetation region does not conform to the model. In addition, because the scattering of the vegetation area shows a high degree of randomness, the selection of the reference axis is affected, and high noise performance of the extended result is caused. Therefore, it makes no sense to select the reference axis when estimating the orientation angle of the vegetation area. More essentially, due to the coverage of the vegetation on the ground surface, the orientation condition of the ground surface is difficult to reflect really by radar echo, and the estimation of the orientation angle of the vegetation area is difficult to carry out accurately. The expanded orientation angle estimation method does not need to expand the orientation angle range of the vegetation area, but increases the error of the orientation angle estimation result.
According to the above analysis, the orientation angle spread of the vegetation area should be excluded, and it is reasonable that the spread method is applied only to the surface scattering target. It is therefore important how to distinguish vegetation areas from bare surface areas. The invention provides a method for self-adaptive distinguishing by using scattering similarity entropy parameters. The scattering similarity entropy Hs is a parameter proposed by Li and Zhang that is related to the randomness and scattering properties of the target scattering, but not to the orientation of the target. Its physical significance is to reflect the randomness of the scattering of the target: the deterministic target has Hs 0, which represents completely non-random scattering; and a completely random target has Hs 1, indicating that the scattering of the target is completely uncertain. Theoretical analysis and experimental verification prove that Hs has the same physical meaning as polarization entropy, so that Hs is less than 0.31345 when the target is Bragg surface scattering. Based on this, the self-adaptive expanding method provided by the invention also utilizes Hs <0.31345 as the criterion of Bragg surface scattering: the scatterers satisfying this condition are subjected to angle expansion, and the scatterers not satisfying the condition are not expanded.
In step 2), the Huynen parameter A obtained according to step 1)0,B0B, C, D, E, F, G and H, and calculating a target scattering similarity entropy parameter Hs; wherein the content of the first and second substances,
the formula for calculating the scattering similarity entropy Hs is as follows:
wherein Hs belongs to [0,1 ]. As can be seen from the formula (4), Hs is convenient to calculate, and feature decomposition or other complex operations are not required, so that the calculation cost is effectively reduced.
The data in this example was solved for scattering similarity entropy Hs, and the result is shown in fig. 5. Comparing the schematic diagram of fig. 2, it can be seen that the region with higher Hs has a very high goodness of fit with the vegetation covered region, which indicates that it is effective to adopt the scattering similarity entropy parameter to identify the vegetation region.
In step 3), self-adaptive expansion selection of orientation angle estimation is performed based on the scattering similarity entropy Hs obtained in step 2). And (4) judging a parameter Hs to distinguish the vegetation area from the bare earth surface.
If Hs is larger than or equal to 0.31345, the randomness of the polarization data is high and is obtained by vegetation scattering, and the orientation angle without a specific reference axis is calculated by using Huynen parameters B and E by adopting a traditional estimation methodWherein the content of the first and second substances,
calculation of orientation angles without specific reference axes using conventional methodsThe calculation formula of (2) is as follows:
if Hs is less than 0.31345, performing expanded orientation angle estimation on the surface scattering target so as to achieve the purposes of expanding the orientation angle estimation range and accurately estimating the orientation angle; then the orientation angle based on the Huynen parameter C, H and no specific reference axisCalculating an adaptive expansion selection parameter C':
based on the Huynen parameters B, E, C, H and the adaptive expansion selection parameter C', adopting expanded orientationThe angle estimation method is extended to the included angle between the vertical polarization axis v, namely the extended orientation angle estimation
Wherein the content of the first and second substances,the method is characterized in that the result obtained by using the traditional orientation angle estimation method can judge the orientation angle without a specific reference axis according to the positive and negative of the parameter CThe reference axis of the target orientation angle is calculated and expanded by uniformly taking the vertical polarization axis v as the reference axis. This time is:
in step 4), the final adaptively expanded earth surface orientation angle estimation is obtained by using the result of the step 3)By combining formula (5) with formula (6), the resulting surface orientation angle estimateThe expression is as follows:
FIG. 6 is a table orientation angle estimation of the final estimation resultThe orientation angle image obtained by the DEM has high consistency with the orientation angle image obtained by the DEM, can accurately reflect the fluctuation change of the terrain, has an expanded value range, avoids the angle winding problem, overcomes the high noise defect of an expansion method, and eliminates the interference of a vegetation area.
The invention also provides a surface orientation angle estimation system based on scattering similarity entropy self-adaptive expansion, which comprises the following components: the device comprises a coherent matrix acquisition module, a parameter calculation module, a scattering similarity entropy calculation module, a ground surface state distinguishing module and a ground surface orientation angle estimation module; the coherent matrix acquisition module is used for acquiring a coherent matrix [ T ] of a target according to polarization data of the full-polarization synthetic aperture radar](ii) a The parameter calculation module is used for calculating the parameter according to the coherent matrix [ T]Calculating a Huynen parameter; the scattering similarity entropy calculation module is used for solving a standard scattering similarity entropy parameter Hs according to the Huynen parameter; the earth surface state distinguishing module is used for distinguishing earth surface states by scattering similar entropy parameters, and the earth surface states comprise earth surface vegetation areas and earth surface exposed areas; the earth surface orientation angle estimation module is used for carrying out traditional orientation angle estimation or expanded orientation angle estimation on the earth surface orientation angle according to the earth surface state to obtain accurate earth surface orientation angle estimation
The invention also provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor implements the method when executing the computer program.
The invention also proposes a computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, causes the processor to carry out the above-mentioned method.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. A surface orientation angle estimation method based on scattering similarity entropy self-adaptive expansion comprises the following steps:
obtaining a coherent matrix of a target according to polarization data of the fully-polarized synthetic aperture radar;
calculating a Huynen parameter according to the coherent matrix;
calculating a target scattering similar entropy parameter according to the Huynen parameter;
distinguishing earth surface states based on the scattering similarity entropy parameters, wherein the earth surface states comprise earth surface vegetation areas and earth surface bare areas;
calculating orientation angle estimation without a specific reference axis and expanded orientation angle estimation;
and obtaining the earth surface orientation angle estimation according to the earth surface state by combining the orientation angle estimation without the specific reference axis and the expanded orientation angle estimation.
2. The method for estimating the earth surface orientation angle based on the scattering similarity entropy self-adaptive expansion of the claim 1 is characterized in that the coherent matrix [ T ] of the target obtained according to the polarization data of the fully-polarized synthetic aperture radar is as follows:
wherein, T11、T12、T13、T21、T22、T23、T31、T32And T33Is a coherence matrix [ T]Of (2) is used.
3. The method for estimating the earth's surface orientation angle based on scattering similarity entropy adaptive expansion of claim 2,the calculating the Huynen parameter according to the coherent matrix specifically comprises the following steps: a. the0,B0B, C, D, E, F, G and H are respectively:
C=Re{T12}
D=-Im{T12}
E=Re{T23}
F=Im{T23}
G=Im{T13}
H=Re{T13}
wherein Re {. is a real part, and Im {. is an imaginary part.
4. The method for estimating the earth surface orientation angle based on scattering similarity entropy self-adaptive expansion of the claim 3, wherein the calculating the target scattering similarity entropy parameter according to the Huynen parameter specifically comprises: calculating a scattering similarity entropy parameter Hs:
wherein Hs belongs to [0,1 ].
5. The method for estimating the earth surface orientation angle based on the scattering similarity entropy adaptive expansion of the claim 4, wherein the earth surface states are distinguished based on the scattering similarity entropy parameters, the earth surface states comprise earth surface vegetation areas and earth surface bare areas, and the method specifically comprises the following steps:
if Hs is more than or equal to 0.31345, the ground surface state is a ground surface vegetation area;
and if Hs <0.31345, the ground surface state is a bare ground surface area.
6. The method for estimating the earth surface orientation angle based on scattering similarity entropy adaptive expansion as claimed in claim 5, wherein the calculating of the orientation angle estimation without a specific reference axis and the expanded orientation angle estimation specifically includes: computing orientation angle estimates without specific reference axesComprises the following steps:
orientation angle based on Huynen parameter C, H and no specific reference axisCalculating an adaptive expansion selection parameter C':
selecting a parameter C' according to self-adaptive expansion, and determining the orientation angle of a non-specific reference axisExpanding to an included angle between the vertical polarization axis v and obtaining an expanded orientation angle
7. the method for estimating the earth surface orientation angle based on scattering similarity entropy self-adaptive expansion as claimed in claim 6, wherein the obtaining of the earth surface orientation angle estimation according to the earth surface state by combining the orientation angle estimation without a specific reference axis and the expanded orientation angle estimation specifically comprises:
if the earth surface state is the earth surface vegetation area, estimating the earth surface orientation angleOrientation angle estimation for no specific reference axis
If the earth surface state is an earth surface bare region, estimating the earth surface orientation angleOrientation angle estimation for extendedNamely:
8. a scattering similarity entropy adaptive expansion-based earth surface orientation angle estimation system is characterized by comprising: the device comprises a coherent matrix acquisition module, a parameter calculation module, a scattering similarity entropy calculation module, a ground surface state distinguishing module and a ground surface orientation angle estimation module;
the coherent matrix acquisition module is used for acquiring a coherent matrix of a target according to polarization data of the full-polarization synthetic aperture radar;
the parameter calculation module is used for calculating a Huynen parameter according to the coherent matrix;
the scattering similar entropy calculation module is used for solving scattering similar entropy parameters according to the Huynen parameters;
the earth surface state distinguishing module is used for distinguishing earth surface states by scattering similar entropy parameters, and the earth surface states comprise earth surface vegetation areas and earth surface exposed areas;
the earth surface orientation angle estimation module is used for calculating the orientation angle estimation without the specific reference axis and the expanded orientation angle estimation, and obtaining the earth surface orientation angle estimation according to the earth surface state and the orientation angle estimation without the specific reference axis and the expanded orientation angle estimation.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method of any of claims 1-7 when executing the computer program.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program which, when executed by a processor, causes the processor to carry out the method of any one of claims 1-7.
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