Real-time infrared imaging simulation method and system based on hardware pipeline acceleration

Abstract

This invention discloses a real-time infrared imaging simulation method and system based on hardware pipeline acceleration. The method comprises the following steps: precalculating the data required for the infrared simulation process, calculating the radiation distribution in the infrared simulation scene using a real-time ray tracing hardware rendering pipeline, simulating the detector effect of the infrared imaging device, and generating the final infrared simulation image. By using the precalculated infrared data as input and leveraging the acceleration of real-time ray tracing technology in the rendering pipeline, the method can simulate and generate an infrared image of the scene in real time.

Description

Technical Field

[0001] The present invention belongs to infrared simulation technology, specifically a real-time ray tracing technology based on the hardware pipeline. According to the temperature field data of the target and background, the radiation brightness value is calculated by comprehensively considering the influence of the environment and atmosphere, and finally an infrared simulation image of the corresponding band is generated. Background Art

[0002] Infrared imaging is the scientific study of how to effectively detect infrared radiation from objects and convert this information into perceptible image signals. Typically, a 3D rendering engine is used on a computer to construct a virtual scene, calculate radiation energy, and simulate the imaging process to generate physically accurate infrared images. In the past two years, advances in hardware and the development of real-time ray tracing technology have made real-time rendering possible using ray tracing algorithms, resulting in even more accurate scene rendering.

[0003] Infrared imaging technology is widely used for target detection, but its image quality is affected by the detection band, meteorological conditions, and sensor hardware parameters. Generating infrared images that account for these diverse factors consumes considerable time and human resources, making it crucial to employ computer-generated infrared simulation within a 3D rendering engine. However, rapid infrared simulation in complex scenes with terrain, buildings, and vehicles requires a significant amount of computation. To generate infrared images in real time based on viewpoint movement or simulated target motion during 3D simulation, previous studies have reduced computational complexity by considering only direct radiation or a single reflection during real-time image generation. However, this approach does not conform to the physical laws of radiant energy propagation, resulting in inaccurate radiant energy calculations in the generated infrared images. Summary of the Invention

[0004] In order to address the shortcomings of existing methods, the purpose of the present invention is to provide an infrared imaging simulation method that can calculate the infrared radiation of an object based on the object's temperature field data, simulate the sensor effect of the infrared imaging device, and generate an infrared simulation image.

[0005] In order to achieve the above objectives, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a real-time infrared imaging simulation method based on hardware pipeline acceleration, comprising the following steps:

[0007] Step 1: Precalculate the data required for the infrared simulation process, including the temperature field of the simulation background and target, surface material parameters, solar radiation, ambient radiation, atmospheric transmittance and path radiation during the simulation period, and make them into texture images;

[0008] Step 2: Use the real-time ray tracing hardware rendering pipeline to calculate the radiation distribution in the infrared simulation scene;

[0009] Step 3, simulating the detector effect of infrared imaging equipment;

[0010] Step 4: Generate the final infrared simulation image.

[0011] In one embodiment, the data required for the pre-calculation of infrared simulation process is as follows:

[0012] Model the simulation background and target, divide their surface materials, and calculate the temperature field data of the corresponding model;

[0013] Calculate the solar radiation, ambient radiation, atmospheric transmittance and path radiation data of the scene during the simulation process.

[0014] In one embodiment, the real-time ray tracing hardware rendering pipeline is used to calculate the radiation distribution in the infrared simulation scene. The specific method is:

[0015] Step 2.1. In the rendering engine's real-time ray tracing rendering pipeline, add a global RenderTarget object to store the precomputed texture lookup table. Add a Uniform variable and associate it with the RenderTarget object. When the program loads the precomputed data, the shader in the rendering pipeline accesses the precomputed texture lookup table through the associated Uniform variable. When the simulation starts, load the simulation data precomputed in Step 1 and start generating rays to emit and trace them into the scene.

[0016] Step 2.2: When the light intersects the model surface, the material number information at the point on the object's surface is obtained through the object's material texture. Combined with the input temperature texture, the spontaneous radiation of the object is calculated by multiplying its own emissivity by the radiation of a black body at the corresponding temperature.

[0017] Step 2.3. Calculate the solar radiation and ambient radiation received by the object. The pre-calculated solar radiation data format is the solar radiation value when the object is at different altitudes and at different zenith angles to the sun. The pre-calculated ambient radiation value is the ambient radiation value received by the scene at different zenith angles. During the simulation, query the pre-calculated data based on the object's position and observation position to obtain the values ​​of these two items.

[0018] Step 2.4: According to the real-time ray tracing rendering pipeline, when a ray hits a surface in the scene, the ray's exit direction and half-angle vector are calculated based on the ray's incident direction and the surface's material information. The reflected radiant energy is then calculated using the Sandford-Robertson BRDF. The reflected ray is then traced to calculate its energy propagation in the scene until it is absorbed or the number of reflections exceeds a certain limit.

[0019] Step 2.5: The infrared radiation of the objects in the simulation scene is summed up by the results calculated in the above steps.

[0020] In one embodiment, the specific method for generating an infrared image is:

[0021] When setting up the simulation, select the corresponding simulation background, scene model, and simulation environment data, and then set the imaging resolution and field of view information; after starting the simulation, generate the corresponding infrared simulation image based on the simulation data.

[0022] In a second aspect, the present invention further provides a real-time infrared imaging simulation system based on hardware pipeline acceleration, comprising:

[0023] The first module is used to pre-calculate the data required in the infrared simulation process, including the temperature field of the simulation background and target, surface material parameters, solar radiation, ambient radiation, atmospheric transmittance and path radiation during the simulation period, and produce texture images;

[0024] The second module uses a real-time ray tracing hardware rendering pipeline to calculate the radiation distribution in the infrared simulation scene;

[0025] The third module is used to simulate the detector effect of infrared imaging equipment;

[0026] The fourth module is used to generate the final infrared simulation image.

[0027] In a third aspect, the present application further provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method described in the first aspect above when executing the program.

[0028] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect above.

[0029] In a fifth aspect, the present application also provides a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, the method described in the first aspect above is implemented.

[0030] Compared with the existing technology, the present invention has the following significant advantages: by using pre-calculated infrared data as input, based on the acceleration of real-time ray tracing in the rendering pipeline, the present invention uses the infrared radiation calculation equation in the rendering pipeline to quickly calculate the infrared radiation in the scene, and then uses the modulation transfer function method to simulate the sensor effect of the infrared imaging device. When the resolution of the simulation program is set to 1920*1080, the rendering frame rate can reach 30FPS, and the infrared image of the scene can be generated by real-time simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is the real-time infrared imaging simulation flow chart.

[0032] Figure 2 Schematic diagram of various stages of an embodiment. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0034] Infrared imaging technology is widely used for target detection, but its image quality is affected by the detection band, meteorological conditions, and sensor hardware parameters. Generating infrared images that account for these diverse factors consumes considerable time and human resources, making it crucial to employ computer-generated infrared simulation within a 3D rendering engine. However, rapid infrared simulation in complex scenes with terrain, buildings, and vehicles requires a significant amount of computation. To generate infrared images in real time based on viewpoint movement or simulated target motion during 3D simulation, previous studies have reduced computational complexity by considering only direct radiation or a single reflection during real-time image generation. However, this approach does not conform to the physical laws of radiant energy propagation, resulting in inaccurate radiant energy calculations in the generated infrared images.

[0035] In view of this, the present application provides a real-time infrared imaging simulation method based on hardware pipeline acceleration, comprising the following steps:

[0036] Step 1: Pre-calculate the data required for the infrared simulation process, including the temperature field of the simulation background and target, surface material parameters, solar radiation, ambient radiation, atmospheric transmittance and path radiation during the simulation period, and make them into texture images. The data required for the pre-calculation of the infrared simulation process are:

[0037] Step 1.1: Model the simulation background and target, divide their surface materials, and calculate the temperature field data of the corresponding model;

[0038] Step 1.2: Calculate the solar radiation, ambient radiation, atmospheric transmittance and path radiation data of the scene during the simulation process.

[0039] Step 2: Use the real-time ray tracing hardware rendering pipeline to calculate the radiation distribution in the infrared simulation scene. The specific method is as follows:

[0040] Step 2.1: In the rendering engine's real-time ray tracing rendering pipeline, add a global RenderTarget object to store the pre-calculated texture lookup table. Add a Uniform variable and associate it with the RenderTarget object. When the program loads the pre-calculated data, the shader in the rendering pipeline can access the pre-calculated texture lookup table through the associated Uniform variable. When the simulation starts, load the simulation data pre-calculated in step 1 and start generating rays to launch and trace them into the scene.

[0041] Step 2.2: When the light intersects the model surface, the material number information at the point on the object's surface is obtained through the object's material texture. Combined with the input temperature texture, the object's spontaneous radiation is calculated by multiplying its own emissivity by the radiation of a black body at the corresponding temperature. The self-radiation can be written as:

[0042] L e (p→ω o )=εM B

[0043] L e (p→ω o ) represents the direction from point p on the surface of the object to ω o The spontaneous radiation brightness term emitted in the direction, ε is the band emissivity of the object, M B Represents the blackbody radiation emittance at the corresponding temperature; the pre-calculated data includes the mapping relationship between blackbody radiation emittance and temperature. When calculating this item, the radiation emittance of the blackbody at the corresponding temperature is obtained by looking up the table.

[0044] Step 2.3: Calculate the solar radiation and ambient radiation received by the object. The pre-calculated solar radiation data format is the solar radiation value when the object is at different altitudes and at different zenith angles to the sun; the pre-calculated ambient radiation value is the ambient radiation value received by the scene at different zenith angles. During the simulation, query the pre-calculated data based on the object's position and observation position to obtain the values ​​of these two items;

[0045] Step 2.4: According to the real-time ray tracing rendering pipeline, when a ray hits the surface of an object in the scene, the ray's exit direction and half-angle vector information are calculated based on the ray's incident direction and the material information of the object's surface. The reflected radiant energy is calculated using the Sandford-Robertson BRDF. The reflected ray is then traced to calculate its energy propagation in the scene until the ray is absorbed or the number of reflections exceeds the specified limit.

[0046] Step 2.5: The infrared radiation of the objects in the simulation scene is summed up by the results calculated in the above steps, that is:

[0047]

[0048] Where L e (p→ω o ) represents the direction from point p to ω on the object o Directional self-radiation, L e (p→ω o ) represents the direction from point p on the surface of the object to ω o The spontaneous radiation brightness term emitted in the direction, π is pi, ρ d_env is the diffuse reflectance, E env (p) and E sun (p) represents the radiation power per unit area of ​​ambient radiation and solar radiation, L i (p←ω i ) represents the influence of other radiation sources, f r (p,ω i →ω o ) is the BRDF term; (n·ω i ) represents the cosine value of the surface normal and the incident light, p(ω i ) represents the distribution function of the incident light; the calculated energy takes into account the atmospheric transmittance and the path radiation received during the transmission process, where τ(θ) represents the atmospheric transmittance, L path represents the path radiation, L o (p→ω o ) represents the direction of the point on the surface of the object o The radiation value emitted in the direction, L o_atmos Indicates the result of the radiation value after atmospheric effect:

[0049] L o_atmos =τ(θ)L o (p→ω o )+L path

[0050] Step 3: Simulate the detector effect of infrared imaging equipment.

[0051] In one embodiment, the specific method of the infrared sensor signal processing process is:

[0052] According to the optical transmittance and vignetting coefficient parameters of the infrared imaging device sensor optical system; the noise coefficient of the detector system module parameters; the voltage gain and grayscale value mapping of the circuit system module parameters; the field of view angle, upper limit of the working band, and lower limit of the working band parameters of the common parameter module; the intermediate data of the calculation process in this step are made into different texture data, and these texture data are sampled in the rendering pipeline to simulate the calculation of the infrared imaging device detector effect.

[0053] Step 4: Generate the final infrared simulation image.

[0054] When setting up the simulation, select the corresponding simulation background, scene model, and simulation environment data, and then set the imaging resolution and field of view information; after starting the simulation, generate the corresponding infrared simulation image based on the simulation data.

[0055] The following is combined with Figure 1 and one The following examples illustrate the steps of the real-time infrared imaging simulation method based on hardware pipeline acceleration of the present application:

[0056] The first step is to pre-calculate multiple temperature textures of the object during the infrared simulation process, and at the same time pre-calculate the solar radiation and environmental radiation data under the simulation conditions to produce a texture image.

[0057] The second step is to add a global RenderTarget object to the real-time ray tracing rendering pipeline of the rendering engine to store the pre-calculated texture lookup table; add a Uniform variable and associate it with the RenderTarget object. When the program loads the pre-calculated data, the shader in the rendering pipeline can access the pre-calculated texture lookup table through the associated Uniform variable. When the simulation starts, load the simulation data pre-calculated in step 1, and start generating rays to emit and trace into the scene; when the ray intersects the model surface, the material number information at the point on the object's surface is obtained through the object's material texture, and combined with the input temperature texture, the object's spontaneous radiation, solar radiation, ambient radiation, and radiation from other radiation sources are calculated.

[0058] The third step is to simulate the detector effect of the infrared imaging device. The typical effects of energy attenuation, imaging vignetting, system imaging noise, and voltage gain caused by the influence of optical system transmittance are simulated.

[0059] The fourth step is to generate the final infrared simulation image. The simulation target is a typical scene, and the infrared imaging simulation band is set to 3~5μm and the imaging resolution is 1920*1080 to generate the infrared simulation image, such as Figure 2The infrared simulation imaging results are shown in the image.

[0060] Based on the same inventive concept, an embodiment of the present invention further provides a real-time infrared imaging simulation system based on hardware pipeline acceleration, comprising:

[0061] The first module is used to pre-calculate the data required in the infrared simulation process, including the temperature field of the simulation background and target, surface material parameters, solar radiation, ambient radiation, atmospheric transmittance and path radiation during the simulation period, and produce texture images;

[0062] The second module uses a real-time ray tracing hardware rendering pipeline to calculate the radiation distribution in the infrared simulation scene;

[0063] The third module is used to simulate the detector effect of infrared imaging equipment;

[0064] The fourth module is used to generate the final infrared simulation image.

[0065] The specific implementation of each module in the above-mentioned real-time infrared imaging simulation system is the same as the steps of the above-mentioned real-time infrared imaging simulation method, and will not be repeated here.

[0066] Each module in the above-mentioned real-time infrared imaging simulation system can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in the computer device in the form of software, so that the processor can call and execute the corresponding operations of each module.

[0067] In one embodiment, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned real-time infrared imaging simulation method based on hardware pipeline acceleration when executing the program.

[0068] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, the real-time infrared imaging simulation method based on hardware pipeline acceleration is implemented.

[0069] In one embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the computer program implements the above-mentioned real-time infrared imaging simulation method based on hardware pipeline acceleration.

[0070] It should be noted that the user-related information (including but not limited to user device information, user personal information, etc.) and user-related data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0071] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processor involved in the various embodiments provided herein may be, but are not limited to, a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic unit, a data processing logic unit based on quantum computing, and the like.

[0072] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0073] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A real-time infrared imaging simulation method based on hardware pipeline acceleration, characterized in that: The steps include: Step 1: Precalculate the data required for the infrared simulation process, including the temperature field of the simulation background and target, surface material parameters, solar radiation, ambient radiation, atmospheric transmittance and path radiation during the simulation period, and make them into texture images; Step 2: Use the real-time ray tracing hardware rendering pipeline to calculate the radiation distribution in the infrared simulation scene. The specific method is as follows: Step 2.

1. In the rendering engine's real-time ray tracing rendering pipeline, add a global RenderTarget object to store the precomputed texture lookup table. Add a Uniform variable and associate it with the RenderTarget object. When the program loads the precomputed data, the shader in the rendering pipeline accesses the precomputed texture lookup table through the associated Uniform variable. When the simulation starts, load the simulation data precomputed in Step 1 and start generating rays to emit and trace them into the scene. Step 2.2: When the light intersects the model surface, the material number information at the point on the object's surface is obtained through the object's material texture. Combined with the input temperature texture, the spontaneous radiation of the object is calculated by multiplying its own emissivity by the radiation of a black body at the corresponding temperature. Step 2.

3. Calculate the solar radiation and ambient radiation received by the object. The pre-calculated solar radiation data format is the solar radiation value when the object is at different altitudes and at different zenith angles to the sun. The pre-calculated ambient radiation value is the ambient radiation value received when observing the scene at different zenith angles. During the simulation, query the pre-calculated data based on the object's position and observation position to obtain the solar radiation and ambient radiation values. Step 2.4: According to the real-time ray tracing rendering pipeline, when a ray hits a surface in the scene, the ray's exit direction and half-angle vector are calculated based on the ray's incident direction and the surface's material information. The reflected radiant energy is then calculated using the Sandford-Robertson BRDF. The reflected ray is then traced to calculate its energy propagation in the scene until it is absorbed or the number of reflections exceeds a certain limit. Step 2.5: The infrared radiation of the objects in the simulation scene is summed up by the results calculated from steps 2.2 to 2.4; Step 3, simulating the detector effect of infrared imaging equipment; Step 4: Generate the final infrared simulation image.

2. The real-time infrared imaging simulation method based on hardware pipeline acceleration according to claim 1, characterized in that: The data required for the pre-calculation infrared simulation process are as follows: Model the simulation background and target, divide their surface materials, and calculate the temperature field data of the corresponding model; Calculate the solar radiation, ambient radiation, atmospheric transmittance and path radiation data of the scene during the simulation process.

3. The real-time infrared imaging simulation method based on hardware pipeline acceleration according to claim 1, characterized in that: The spontaneous radiation emitted by an object is: L e (p→ω o )=εM B L e (p→ω o ) represents the direction from point p on the surface of the object to ω o The spontaneous radiation brightness term emitted in the direction, ε is the band emissivity of the object, M B Represents the blackbody radiation emittance at the corresponding temperature; the pre-calculated data includes the mapping relationship between the blackbody radiation emittance and temperature. When calculating the mapping relationship between the blackbody radiation emittance and temperature, the radiation emittance of the blackbody at the corresponding temperature is obtained by looking up the table.

4. The real-time infrared imaging simulation method based on hardware pipeline acceleration according to claim 3, characterized in that: In step 2.5, the infrared radiation of the objects in the simulation scene is summed up by the results calculated in steps 2.2 to 2.4, that is: Where L o (p→ω o ) represents the direction from point p to ω on the object o Directional self-radiation, L e (p→ω o ) represents the direction from point p on the surface of the object to ω o The spontaneous radiation brightness term emitted in the direction, π is pi, ρ d_env is the diffuse reflectance, E env (p) and E sun (p) represents the radiation power per unit area of ​​ambient radiation and solar radiation, L i (p←ω i ) represents the influence of other radiation sources, f r (p,ω i →ω o ) is the BRDF term; (n·ω i ) represents the cosine value of the surface normal and the incident light, p(ω i ) represents the distribution function of incident light; L o_atmos =τ(θ)L o (p→ω o )+L path Where τ(θ) represents the atmospheric transmittance, L path represents the path radiation, L o_atmos Indicates L o (p→ω o )The result after atmospheric effects.

5. The real-time infrared imaging simulation method based on hardware pipeline acceleration according to claim 1, characterized in that: The specific method for generating infrared images is: When setting up the simulation, select the corresponding simulation background, scene model, and simulation environment data, and then set the imaging resolution and field of view information; after starting the simulation, generate the corresponding infrared simulation image based on the simulation data.

6. A real-time infrared imaging simulation system based on hardware pipeline acceleration, characterized in that: include: The first module is used to pre-calculate the data required in the infrared simulation process, including the temperature field of the simulation background and target, surface material parameters, solar radiation, ambient radiation, atmospheric transmittance and path radiation during the simulation period, and produce texture images; The second module is used to calculate the radiation distribution in the infrared simulation scene using the real-time ray tracing hardware rendering pipeline. The specific calculation steps are as follows: (1) In the real-time ray tracing rendering pipeline of the rendering engine, a global RenderTarget object is added to store the pre-calculated texture lookup table; a Uniform variable is added and associated with the RenderTarget object. When the program loads the pre-calculated data, the shader in the rendering pipeline accesses the pre-calculated texture lookup table through the associated Uniform variable; when the simulation starts, the pre-calculated simulation data in the first module is loaded, and light rays are generated and emitted into the scene for tracing; (2) When the light intersects the model surface, the material number information at the point on the object's surface is obtained through the object's material texture. Combined with the input temperature texture, the spontaneous radiation of the object is calculated by multiplying its own emissivity by the radiation of a black body at the corresponding temperature; (3) Calculate the solar radiation and environmental radiation received by the object; the pre-calculated solar radiation data format is the solar radiation value when the object is at different altitudes and at different zenith angles to the sun; the pre-calculated environmental radiation value is the environmental radiation value received when observing the scene at different zenith angles; during the simulation process, query the pre-calculated data according to the position of the object and the observation position to obtain the values ​​of solar radiation and environmental radiation; (4) According to the real-time ray tracing rendering pipeline, when a ray hits the surface of an object in the scene, the ray's exit direction and half-angle vector information are calculated based on the ray's incident direction and the material information of the object's surface, and the reflected radiant energy is calculated using the Sandford-Robertson BRDF. The reflected ray is then traced to calculate its energy propagation in the scene until the ray is absorbed or the number of reflections exceeds a certain limit. (5) The infrared radiation of the objects in the simulation scene is summed up by the results calculated in steps (2) to (4); The third module is used to simulate the detector effect of infrared imaging equipment; The fourth module is used to generate the final infrared simulation image.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

Images