Image reconstruction method and device

Abstract

The invention discloses an image reconstruction method and device, and relates to the technical field of transmission electron microscopic image processing. The method comprises the steps that a frequency domain space image of a to-be-analyzed material is corrected, and the frequency domain space image is obtained by conducting Fourier transform on an image set, collected in an STEM-EELS mode, of the to-be-analyzed material; extracting image information of the corrected frequency domain space image, and determining a peak value position in the corrected frequency domain space image of the to-be-analyzed material; generating a coordinate transformation matrix for image pixel points based on the extracted image information and peak position; and performing image reconstruction on the image set of the to-be-analyzed material by using the coordinate transformation matrix. According to the scheme provided by the embodiment of the invention, the resolution and precision of the microscopic image of the material with weaker irradiation resistance or beam sensitivity are effectively improved, and the precise analysis of the local microscopic structure of the material with weaker irradiation resistance or beam sensitivity is facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of transmission electron microscopy image processing, and in particular, to an image reconstruction method and apparatus. Background Art

[0002] The scanning transmission electron microscopy (STEM) mode of a transmission electron microscope (TEM) is an important means for analyzing the microscopic morphology and microstructure of materials (such as elemental distribution, valence bond information, etc.). However, for materials with weak radiation resistance or beam-sensitive materials (such as zeolites, MOFs (metal organic frameworks), polymers, halide perovskites, etc.), during the TEM scanning process, radiation damage will occur, and the radiation damage will affect the characterization of the microstructure. Currently, mainly by combining STEM with electron energy loss spectroscopy (EELS) to collect image data of materials with weak radiation resistance or beam-sensitive materials under weak light, in order to reveal the microstructure, oxidation state, local electronic structure, chemical distribution, etc. of materials with weak radiation resistance or beam-sensitive materials.

[0003] Currently, mainly the principle components analysis method (PCA) is used to extract the principal components in the image data collected by STEM-EELS. However, due to a large amount of noise in the image data collected under weak light, the noise will distort the calculation results, resulting in incorrect extraction of the principal components, resulting in poor resolution, accuracy, and analytical accuracy of the microstructure of the material. Summary of the Invention

[0004] In view of this, embodiments of the present invention provide an image reconstruction method and apparatus. The solution provided by the embodiments of the present invention can effectively improve the resolution and accuracy of the microscopic images of materials with weak radiation resistance or beam-sensitive materials, which is beneficial to the accurate analysis of the local microscopic structure of materials with weak radiation resistance or beam-sensitive materials.

[0005] To achieve the above object, according to the first aspect of the embodiments of the present invention, an image reconstruction method is provided, including:

[0006] Correcting the frequency domain spatial image of the material to be analyzed, where the frequency domain spatial image is obtained by performing a Fourier transform on an image set of the material to be analyzed collected in the STEM-EELS mode;

[0007] Extract the image information of the corrected frequency-domain spatial image, and determine the peak position in the corrected frequency-domain spatial image of the material to be analyzed;

[0008] Generate a coordinate transformation matrix for the image pixel points based on the extracted image information and the peak position;

[0009] Use the coordinate transformation matrix to perform image reconstruction on the image set of the material to be analyzed.

[0010] Optionally, the image reconstruction method further includes: performing preliminary noise reduction processing on the image set of the material to be analyzed collected in the STEM-EELS mode;

[0011] Perform Fourier transform on the preliminarily noise-reduced image to obtain the frequency-domain spatial image corresponding to the material to be analyzed.

[0012] Optionally, correcting the frequency-domain spatial image of the material to be analyzed includes:

[0013] Select at least two diffraction spots in the frequency-domain spatial image, and adjust the selected at least two diffraction spots;

[0014] Based on the adjusted diffraction spots, correct the frequency-domain spatial image of the material to be analyzed.

[0015] Optionally, determining the peak position in the corrected frequency-domain spatial image of the material to be analyzed includes:

[0016] In the corrected frequency-domain spatial image of the material to be analyzed, search for the peaks and corresponding coordinates of the diffraction spots included in the frequency-domain spatial image.

[0017] Optionally, the above image reconstruction method further includes:

[0018] For the image pixel points included in the image information that are related to the peak position, respectively construct fitting curves of the image pixel points in the x direction and the y direction;

[0019] Use the fitting curves of each image pixel point in the x direction and the y direction to calculate the extreme point coordinates of each image pixel point, and use the extreme point coordinates to correct the peak position;

[0020] Generating a coordinate transformation matrix for the image pixel points includes:

[0021] Use the corrected peak position and its corresponding image information to construct a linear coordinate transformation matrix.

[0022] Optionally,

[0023] Said separately constructing fitting curves of the image pixel points in the x-direction and y-direction includes:

[0024] Finding the previous pixel point and the next pixel point of the image pixel point in the x-direction, and constructing a parabolic curve of the image pixel point in the x-direction by using the previous pixel point and the next pixel point in the x-direction and the pixel value of the image pixel point;

[0025] Finding the previous pixel point and the next pixel point of the image pixel point in the y-direction, and constructing a parabolic curve of the image pixel point in the y-direction by using the previous pixel point and the next pixel point in the y-direction and the pixel value of the image pixel point.

[0026] Optionally, said constructing a linear coordinate transformation matrix includes:

[0027] Taking the central position of the frequency domain space image as the coordinate origin, and translating the pixel point at the corrected peak position;

[0028] Generating a coordinate transformation matrix by using the original coordinate value of the peak position and the coordinate value of the peak position in the coordinate system with the central position of the frequency domain space image as the coordinate origin.

[0029] In a second aspect, an embodiment of the present invention provides an image reconstruction device, including: a correction unit, a coordinate transformation unit, and a reconstruction unit, wherein,

[0030] The correction unit is configured to correct the frequency domain space image of the material to be analyzed, wherein the frequency domain space image is obtained by performing a Fourier transform on an image set collected from the material to be analyzed in the STEM-EELS mode;

[0031] The matrix construction unit is configured to extract the image information of the corrected frequency domain space image, and determine the peak position in the corrected frequency domain space image of the material to be analyzed; generating a coordinate transformation matrix for the image pixel points based on the extracted image information and the peak position;

[0032] The reconstruction unit is configured to perform image reconstruction on the image set of the material to be analyzed by using the coordinate transformation matrix.

[0033] In a third aspect, an embodiment of the present invention provides an electronic device, including:

[0034] One or more processors;

[0035] A storage device for storing one or more programs,

[0036] When the one or more programs are executed by the one or more processors, the one or more processors implement the method provided in the embodiment of the first aspect as described above.

[0037] In a fourth aspect, an embodiment of the present invention provides a computer-readable medium, on which a computer program is stored, and when the program is executed by a processor, the method provided in the embodiment of the first aspect as described above is implemented.

[0038] One embodiment of the above invention has the following advantages or beneficial effects: By correcting the frequency-domain spatial image of the material to be analyzed, the corrected frequency-domain spatial image can more accurately indicate the crystal phase index of the image of the material to be analyzed through the position of the diffraction spots. The center position of the diffraction spot or the position with the largest pixel value in the diffraction spot generally corresponds to the peak value of the corrected frequency-domain spatial image. Based on this, by extracting the image information of the corrected frequency-domain spatial image and the peak position in the frequency-domain spatial image of the material to be analyzed, it is possible to initially locate the center position of the diffraction spot or the position with the largest pixel value in the diffraction spot and the image information of the diffraction spot in the frequency-domain spatial image. Since the offset directions of the individual pixel points in the image set are basically the same, subsequently, based on the extracted image information and peak position, a coordinate transformation matrix is generated for the image pixel points, which can more accurately reflect the transformation of the image pixel points. Then, using the coordinate transformation matrix, image reconstruction is performed on the image set of the material to be analyzed, which can retain as many image pixel points as possible, effectively improving the resolution and accuracy of the microscopic images of materials with weak radiation resistance or beam sensitivity, and facilitating the precise analysis of the local microscopic structure of materials with weak radiation resistance or beam sensitivity.

[0039] The further effects of the above non-conventional optional methods will be described in conjunction with specific embodiments below. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings are used to better understand the present invention and do not constitute an improper limitation to the present invention. Among them:

[0041] Figure 1 is a schematic diagram of the main process of the image reconstruction method according to an embodiment of the present invention;

[0042] Figure 2 is a two-dimensional image in an image set collected in the STEM-EELS mode of a molecular sieve according to an embodiment of the present invention;

[0043] Figure 3 is corresponding to according to an embodiment of the present invention Figure 2 shown two-dimensional image of the frequency-domain spatial image;

[0044] Figure 4 is according to the present invention Figure 3The corrected frequency-domain space image obtained after correcting the shown frequency-domain space image;

[0045] Figure 5 It is a schematic diagram of the main process of an image reconstruction method according to another embodiment of the present invention;

[0046] Figure 6 It is a schematic diagram of the main units of an image reconstruction device according to an embodiment of the present invention;

[0047] Figure 7 It is a schematic diagram of the system structure on which the embodiment of the present invention depends;

[0048] Figure 8 It is a schematic diagram of the structure of a computer system of a terminal device or a server suitable for implementing the embodiment of the present invention. Detailed implementation manners

[0049] TEM generally uses a high-energy electron beam accelerated by high voltage as the incident light source. The high-energy electron beam is deflected and converged step by step by electromagnetic lenses, irradiated onto an extremely thin sample material, and different signals are obtained by using the interaction between the electron beam and the substance, such as transmitted electrons, elastic scattering and inelastic scattering electrons, characteristic X-rays, etc. These different signals can reflect the structural characteristics and physical and chemical characteristics of the material. Therefore, imaging the microstructure based on these signals can visually display the microstructure. In addition, by analyzing these signals, information such as elements, valence states, and coordination can also be obtained simultaneously. Further, combined with spherical aberration correction in the STEM mode, through a sub-atomic scale electron probe, while obtaining an atomic resolution image, atomic resolution elemental distribution and valence bond information, etc. can be obtained. Combining spherical aberration corrected scanning transmission electron microscopy (STEM) with electron energy loss spectroscopy (EELS) can obtain the valence states and valence bonds of atoms with different coordinations at the atomic scale. However, in order to make the high-energy electron beam have sufficient penetration ability and a shorter wavelength in order to obtain a more accurate and clear microstructure, the incident electron energy of a high-resolution electron microscope is usually 200 kV or 300 kV. For most materials with relatively strong radiation resistance such as metals, ceramics, and semiconductors, these high-energy incident electrons are helpful for detailed research on the microstructure at the atomic scale. However, there are still many important material systems with very weak radiation resistance or beam-sensitive materials, such as zeolites, MOF (metal organic framework), polymers, halide perovskites, etc. Using the above high-energy incident electrons will cause radiation damage to the materials. Therefore, for materials with very weak radiation resistance or beam sensitivity, through weak light (i.e., low-energy incident electrons) collection conditions, we can reveal information such as the nano-scale chemical distribution, oxidation state, and local electronic structure of zeolites, providing important references for the development of new materials with very weak radiation resistance or beam sensitivity.

[0050] For materials with very weak radiation resistance or beam sensitivity currently combined in image and frequency-domain spatial image analysis, the principal component analysis method (PCA) is mainly used. PCA mainly relies on the covariance matrix to extract the principal components. However, a large amount of noise generated under weak light collection conditions will distort the calculation results of the covariance matrix, which will in turn lead to incorrect extraction of the principal components and affect the dimensionality reduction effect. When PCA attempts to capture the main features of the data by maximizing the variance, a large amount of noise also has variance and may be misinterpreted as a useful structure of the data, resulting in inaccurate principal components and inability to effectively distinguish signals from noise. That is, a poor signal-to-noise ratio of the data causes noise to interfere with the effective extraction of the original signal by PCA, distorts the data, and affects subsequent analysis and interpretation. In addition, since PCA can only capture linear relationships in the data, its effect is significantly reduced for data with complex non-linear structures. PCA projects high-dimensional data into a low-dimensional space through linear transformation, which may lead to loss of important feature information. Especially when dealing with complex structures, this information loss will directly affect the accuracy of subsequent analysis. This makes it impossible to fully reveal the true microscopic structural features when dealing with materials such as molecular sieves with very weak radiation resistance or beam sensitivity. Further, because PCA is affected by all data points when calculating the principal components, outliers will cause the deviation of the principal component direction and reduce the reliability of the analysis results. In the analysis of sensitive materials such as molecular sieves, this may lead to misjudgment and incorrect interpretation. Although PCA is a powerful dimensionality reduction technique that can simplify STEM-EELS data, reduce redundant information, and improve computational efficiency, it also has some inherent drawbacks, such as limited ability to handle non-linear relationships, poor interpretability, sensitivity to outliers, high computational complexity, etc.

[0051] To solve the above problems of the existing PCA in the analysis of STEM images and EELS spectrograms for materials with very weak radiation resistance or beam sensitivity, an embodiment of the present invention provides a new image reconstruction method.

[0052] The material to be analyzed involved in the embodiment of the present invention generally refers to materials with relatively weak radiation resistance or beam-sensitive porous crystalline materials, such as the above-mentioned zeolites, MOFs (metal organic frameworks), polymers, halide perovskites, etc.

[0053] The set of images collected in the STEM-EELS mode involved in the embodiment of the present invention refers to two-dimensional images collected in the STEM-EELS mode.

[0054] The exemplary embodiments of the present invention will be described below with reference to the accompanying drawings. Various details of the embodiments of the present invention are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. Similarly, descriptions of well-known functions and structures are omitted in the following description for clarity and conciseness.

[0055] Specifically, as Figure 1 shown, the image reconstruction method may include the following steps:

[0056] Step S101: Correct the frequency-domain space image of the material to be analyzed, where the frequency-domain space image is obtained by performing a Fourier transform on a set of images collected from the material to be analyzed in the STEM-EELS mode.

[0057] The main process of this correction step is to select at least two diffraction spots in the frequency-domain space image of the material to be analyzed. These diffraction spots are generally formed by the core structure of the main components of the material to be analyzed, such as the lattice of molecular sieves. That is, these diffraction spots can be used as characteristic points in the frequency-domain space image, and the pixel points corresponding to these diffraction spots can be used as characteristic points in the two-dimensional image. By correcting the at least two selected diffraction spots, the characteristic points can be more accurately determined, and the correction of the characteristic points can be achieved, ensuring the accuracy of the information contained in the characteristic points. Preferably, two diffraction spots are selected in this step. Among them, a rectangular frame is drawn on one diffraction spot, and an elliptical frame is drawn on the other diffraction spot. By adjusting the frequency-domain space image, the gray value of the part located within the rectangular frame or the elliptical frame in the diffraction spot is increased, and the gray value of the edge region is decreased. The size of the rectangular frame or the diameter of the elliptical frame can be set according to the area of the diffraction spot.

[0058] Among them, the distance between any two of the at least two selected diffraction spots satisfies the law of periodic structural changes of the material to be analyzed.

[0059] Among them, specifically performing a Fourier transform on the set of images collected from the material to be analyzed in the STEM-EELS mode means performing a Fourier transform on each two-dimensional image in the set of images collected in the STEM-EELS mode to obtain the frequency-domain space image. Exemplarily, taking Figure 2 a two-dimensional image of a certain molecular sieve shown as an example, by performing a Fourier transform on the Figure 2 shown two-dimensional image, the obtained frequency-domain space image is as Figure 3 shown.

[0060] Further, before this step S101, it may also include: calibrating the camera scale in the STEM-EELS mode. Specifically, in the STEM-EELS mode, an image set of a standard sample consistent with the material type to be analyzed is collected. The two-dimensional images in the image set of the standard sample are converted into frequency-domain space images of the standard sample. Two diffraction spots are selected in the frequency-domain space image of the standard sample. One diffraction spot is calibrated and corrected using an elliptical frame, and the other diffraction spot is calibrated and corrected using a rectangular frame (i.e., an elliptical frame or a rectangular frame is drawn in the central area of the diffraction spot). By adjusting the TEM parameters, the diffraction spot is made to enter the drawn elliptical frame or rectangular frame, thereby realizing the calibration and correction of the camera scale. By calibrating and correcting the camera scale using the same type of standard sample, the interference of noise on the image set collected from the material to be analyzed in the STEM-EELS mode can be further reduced.

[0061] This step realizes the overall preliminary correction of the two-dimensional images in the image set through several diffraction spots, and all pixel points in the two-dimensional images can be retained during this correction process.

[0062] Step S102: Extract the image information of the corrected frequency-domain space image, and determine the peak position in the corrected frequency-domain space image of the material to be analyzed.

[0063] Among them, the image information mainly includes the size of the two-dimensional image, pixel values, physical sizes of pixel values, etc.

[0064] Generally speaking, porous crystalline materials generally have a periodically varying structure, and the periodic variation will be manifested as significant peaks in the frequency-domain space image. This peak corresponds to characteristic points in the image information, such as the lattice of molecular sieves. That is to say, through this step, the pixel points corresponding to the diffraction spots in the image information can be found, and the peak positions corresponding to the diffraction spots can be found from the frequency-domain space image. The pixel points corresponding to the diffraction spots and the peak positions corresponding to the diffraction spots can establish a corresponding relationship based on the diffraction spots. Among them, the peak position is essentially the position of the pixel points corresponding to the diffraction spots located based on the two-dimensional coordinate system constructed with the upper left corner of the two-dimensional image as the coordinate origin.

[0065] Step S103: Generate a coordinate transformation matrix for the image pixel points based on the extracted image information and peak position.

[0066] This step constructs a coordinate transformation matrix based on the pixel points corresponding to the diffraction spots and the peak positions corresponding to the diffraction spots, that is, constructs a coordinate transformation matrix through several key feature points (pixel points corresponding to the diffraction spots) of the two-dimensional image and the peak positions corresponding to these several key feature points. Since the accuracy of these key feature points is relatively high, and the accuracy of the peak positions corresponding to these several key feature points is also relatively high, the constructed coordinate transformation matrix can at least accurately give the coordinate transformation of the key feature points.

[0067] It should be noted that the coordinate transformation matrix in this step transforms the positions of each pixel point in the two-dimensional image from the two-dimensional coordinate system with the upper left corner of the two-dimensional image as the coordinate origin to the two-dimensional coordinate system with the center point of the two-dimensional image as the coordinate origin. During the conversion process, the positions of each pixel point are corrected synchronously.

[0068] Through the above steps S102 and S103, a new peak detection and coordinate transformation method is provided, ensuring the accurate extraction and mapping of key feature points, and laying a foundation for data reconstruction.

[0069] Step S104: Use the coordinate transformation matrix to perform image reconstruction on the image set of the material to be analyzed.

[0070] The technical solution provided by the embodiment of the present invention is based on the diffraction spots of the frequency-domain space image, corrects the frequency-domain space image, enables the diffraction spots to more accurately reflect the key feature points of the material to be analyzed, and through the peak positions in the frequency-domain space image, the position coordinates of the key feature points can be determined. Based on the position coordinates of the key feature points, a coordinate transformation matrix is generated, enabling the coordinate transformation matrix to transform each pixel point in the two-dimensional image into a new coordinate system, and by correcting the frequency-domain space image, the pixel points in the two-dimensional image can be initially corrected, and the positions of each pixel point can be further corrected during the conversion process to improve the accuracy and precision of the reconstructed image.

[0071] That is to say, Figure 1The technical solution provided by the illustrated embodiment can accurately indicate the crystal phase index of the material to be analyzed in the image of the material to be analyzed through the corrected frequency domain spatial image of the material to be analyzed. The central position of the diffraction spot or the position with the largest pixel value in the diffraction spot generally corresponds to the peak value of the corrected frequency domain spatial image. Based on this, by extracting the image information of the corrected frequency domain spatial image and the peak position in the frequency domain spatial image of the material to be analyzed, it is possible to initially locate the central position of the diffraction spot or the position with the largest pixel value in the diffraction spot and the image information of the diffraction spot in the frequency domain spatial image. Since the offset directions of the pixel points in the image set are basically the same, subsequently, based on the extracted image information and peak position, a coordinate transformation matrix is generated for the pixel points of the image, which can more accurately reflect the transformation of the pixel points of the image. Then, using the coordinate transformation matrix to perform image reconstruction on the image set of the material to be analyzed can retain as many pixel points as possible, effectively improving the resolution and accuracy of the microscopic image of materials with weak radiation resistance or beam sensitivity, which is beneficial to the precise analysis of the local microscopic structure of materials with weak radiation resistance or beam sensitivity.

[0072] In addition, the technical solution provided by the embodiment of the present invention realizes high-precision non-destructive analysis of materials under low-dose conditions, providing a reliable technical means for materials science and biological research.

[0073] Furthermore, the above image reconstruction method may further include: performing preliminary noise reduction processing on the image set of the material to be analyzed collected in the STEM-EELS mode; and performing Fourier transform on the preliminarily noise-reduced image to obtain the frequency domain spatial image corresponding to the material to be analyzed. Through the preliminary noise reduction processing, the amount of image data can be reduced and the calculation efficiency can be improved. It should be noted that this preliminary noise reduction processing mainly removes the obvious noise signals in the two-dimensional image.

[0074] In addition, the specific implementation manner of the above step S101 may include: selecting at least two diffraction spots in the frequency domain spatial image and adjusting the selected at least two diffraction spots; based on the adjusted diffraction spots, correcting the frequency domain spatial image of the material to be analyzed. It should be noted that this frequency domain spatial image is obtained by performing Fourier transform on the two-dimensional image after the above preliminary noise reduction processing. The selection and adjustment of the diffraction spots have been described in detail above and will not be elaborated here. For Figure 3 the illustrated frequency domain spatial image, the corrected frequency domain spatial image is as Figure 4 shown.

[0075] Further, the above image reconstruction method may further include: for each image pixel point related to the peak position included in the image information (i.e., the image pixel point corresponding to the diffraction spot in the frequency domain space image, it should be noted that in addition to the above selected at least two diffraction spots, the diffraction spot may also include other unselected diffraction spots), for each image pixel point, respectively construct fitting curves of the image pixel point in the x-direction and the y-direction; use the fitting curves of each image pixel point in the x-direction and the y-direction to calculate the extreme point coordinates of each image pixel point, and use the extreme point coordinates to correct the peak position; generally speaking, compared with the surrounding area of the diffraction spot, the pixel value of the diffraction spot (i.e., the core feature point of the material) is a maximum value. Based on this, by constructing the fitting curves of the image pixel point in the x-direction and the y-direction, the extreme point can be found, which is the pixel point of the diffraction spot. Correspondingly, the position coordinates corresponding to the extreme point are its true coordinate positions. Then, based on this, the peak position can be corrected using the extreme point coordinates to achieve the correction of the frequency domain space image. To improve the position accuracy of the frequency domain space image and the diffraction spot (i.e., the core feature point of the material). Correspondingly, the specific implementation manner of generating the coordinate transformation matrix for the image pixel point includes: using the corrected peak position and its corresponding image information to construct a linear coordinate transformation matrix. This coordinate transformation matrix converts each pixel point in the two-dimensional image from the current coordinate system with the upper left corner of the two-dimensional image as the coordinate origin to the coordinate system with the center point of the two-dimensional image as the coordinate origin. Before the conversion, by using the fitting curves of the image pixel point in the x-direction and the y-direction, the coordinates of the image pixel point in the original coordinate system are corrected to ensure the accuracy of the position coordinates of the image pixel point after the subsequent conversion.

[0076] Specifically, the specific implementation manner of respectively constructing the fitting curves of the image pixel point in the x-direction and the y-direction may include: finding the previous pixel point and the next pixel point of the image pixel point in the x-direction, and using the previous pixel point and the next pixel point in the x-direction and the pixel value of the image pixel point to construct a parabolic curve of the image pixel point in the x-direction; finding the previous pixel point and the next pixel point of the image pixel point in the y-direction, and using the previous pixel point and the next pixel point in the y-direction and the pixel value of the image pixel point to construct a parabolic curve of the image pixel point in the y-direction.

[0077] Exemplarily, taking Figure 2 the shown coordinate system as an example, its x-direction is the horizontal direction and the y-direction is the vertical direction. Then the previous pixel point of the image pixel point in the x-direction refers to the pixel point on the left side of the image pixel point, and the next pixel point of the image pixel point in the x-direction refers to the pixel point on the right side of the image pixel point. The parabolic curve of the image pixel point in the x-direction can be calculated by the following calculation formula (1):

[0078]

[0079] where valX i represents the x - coordinate corresponding to the i - th image pixel on the parabolic curve in the x - direction; represents the pixel value of the previous pixel of the i - th image pixel in the x - direction; represents the pixel value of the next pixel of the i - th image pixel in the x - direction; N i represents the pixel value of the i - th image pixel.

[0080] The parabolic curve of the image pixels in the y - direction can be obtained by the following calculation formula (2):

[0081]

[0082] where valY i represents the x - coordinate corresponding to the i - th image pixel on the parabolic curve in the y - direction; represents the pixel value of the previous pixel of the i - th image pixel in the y - direction; represents the pixel value of the next pixel of the i - th image pixel in the y - direction; N i represents the pixel value of the i - th image pixel.

[0083] Among them, the coordinates of the extreme value of the pixel value corresponding to the image pixels in the x - direction can be obtained by the following calculation formula (3).

[0084]

[0085] where X i represents the x - coordinate value of the precise extreme value after correcting the i - th image pixel; x i represents the x - coordinate value of the i - th image pixel; x i-1 represents the x - coordinate value of the previous pixel of the i - th image pixel; x i+1 represents the x - coordinate value of the next pixel of the i - th image pixel. It should be noted that the y - coordinates of the image pixel corresponding to the x - direction and its previous and next pixels are the same, and the x - coordinates are different.

[0086] Among them, the coordinates of the extreme value of the pixel value corresponding to the image pixels in the y - direction can be obtained by the following calculation formula (4).

[0087]

[0088] where Y i represents the y - coordinate value of the precise extreme value after correcting the i - th image pixel; yi represents the y - coordinate value of the i - th image pixel; y i-1 represents the y - coordinate value of the previous pixel of the i - th image pixel; y i+1 represents the y - coordinate value of the next pixel of the i - th image pixel. It should be noted that for the image pixels in the y - direction, their x - coordinates are the same as those of their previous and next pixels, while the y - coordinates are different.

[0089] By using the above - mentioned calculation formulas (1) and (2), two extreme points corresponding to the i - th image pixel are found (the extreme point in the x - direction and the extreme point in the y - direction). Among them, the ordinate of the extreme point in the x - direction corresponding to the i - th image pixel is the ordinate of the i - th image pixel, and the abscissa is calculated by the above - mentioned calculation formula (3); the abscissa of the extreme point in the y - direction corresponding to the i - th image pixel is the abscissa of the i - th image pixel, and the ordinate of the extreme point in the y - direction is calculated by the above - mentioned calculation formula (4). Taking the two extreme points as subsequent feature points effectively expands the feature points and makes the constructed coordinate transformation matrix more accurate.

[0090] Among them, the exact extreme value after correcting the i - th image pixel and the exact extreme value after correcting the i - th image pixel are obtained, which are the extreme values of the pixel values of the image pixel. Then, the coordinate position corresponding to this extreme value is the exact coordinate position of the accurately located feature point.

[0091] In addition, the above process is essentially to extract the feature points with physical significance in the STEM - EELS data. It is directly related to the actual microstructure, provides higher interpretability and physical connection, helps to deeply understand and analyze the microstructure of materials, and has more practical application value especially in materials science research. And by extracting the feature points with physical significance in the STEM - EELS data, the most important structural information in the data is retained. It retains more microscopic structural details by optimizing the data reconstruction process, especially having obvious advantages in features at smaller scales such as pore structures.

[0092] More specifically, using the corrected peak position and its corresponding image information, the specific implementation of constructing the linear coordinate transformation matrix may include: taking the central position of the frequency - domain space image as the coordinate origin and translating the pixel points of the corrected peak position; using the original coordinate value of the peak position and the coordinate value of the peak position in the coordinate system with the central position of the frequency - domain space image as the coordinate origin to generate the coordinate transformation matrix.

[0093] The specific implementation for the pixel points of the translated and corrected peak position may include: calculating the coordinate transformation parameters and using the calculated coordinate transformation parameters to determine the coordinate value of the peak position in the coordinate system with the central position of the image as the coordinate origin.

[0094] Among them, the coordinate transformation parameters can be calculated using the following calculation formula group (5).

[0095]

[0096] Among them, dx1, dy1, dx2 and dy2 represent the coordinate transformation parameters; k2 represents the scaling parameter of the transformed image in the x direction; k1 represents the scaling parameter of the original image in the x direction; h1 represents the scaling parameter of the original image in the y direction; h2 represents the scaling parameter of the transformed image in the y direction.

[0097] More specifically, the coordinate values of the peak positions in the coordinate system with the center position of the image as the coordinate origin can be calculated using the following calculation formula group (6).

[0098]

[0099] Among them, dx1, dy1, dx2 and dy2 represent the coordinate transformation parameters; (x1′, y1′) and (x2′, y2′) respectively represent the coordinates after transformation of two characteristic pixel points (i.e., two peak positions) in the frequency domain space image; sx represents the width of the frequency domain space image in the x direction; sy represents the height of the frequency domain space image in the y direction.

[0100] By substituting the coordinates of the pixel points of the multiple peak positions after translational correction and the coordinates before translation into the following calculation formula (7), the coordinate transformation matrix parameters a, b, c, d, e, f are calculated.

[0101]

[0102] Among them, represents the coordinates after translation of the pixel points of the peak positions after translational correction (i.e., extreme points); represents the coordinates before translation of the pixel points of the peak positions after correction (i.e., extreme points);

[0103] Subsequently, based on the coordinate transformation matrix parameters a, b, c, d, e, f and the coordinates before translation of the pixel points in the two-dimensional image, the coordinates of the pixel points after translation can be obtained, thereby realizing the reconstruction of the two-dimensional image.

[0104] Furthermore, another embodiment of the present invention provides an image reconstruction method. As Figure 5 shown, the image reconstruction method of this other embodiment may include the following steps:

[0105] Step S501: Collect an image set of a standard sample consistent with the type of the material to be analyzed in the STEM-EELS mode.

[0106] For example, if the material to be analyzed is a molecular sieve, the standard sample is also a molecular sieve with a known structure; if the material to be analyzed is a metal material, the standard sample is also a metal material with a known structure, etc.

[0107] Step S502: Perform preliminary noise reduction processing on the image set of the standard sample collected in the STEM-EELS mode.

[0108] Step S503: Perform Fourier transform on the noise-reduced image set of the standard sample to obtain the frequency domain space image corresponding to the standard sample.

[0109] Step S504: Select two diffraction spots in the frequency domain space image corresponding to the standard sample, and draw an elliptical region and a rectangular region on each of the two diffraction spots respectively. Adjust the diffraction spots based on the elliptical and rectangular regions to correct the frequency domain space image corresponding to the standard sample.

[0110] Step S505: Calibrate the TEM camera scale using a standard sample of the same type as the material to be analyzed.

[0111] Step S506: Based on the calibrated TEM camera scale, collect the image set of the material to be analyzed in the STEM-EELS mode.

[0112] Step S507: Perform preliminary noise reduction processing on the image set of the material to be analyzed.

[0113] Step S508: Perform Fourier transform on the preliminarily noise-reduced image set of the material to be analyzed to obtain the frequency domain space image corresponding to the material to be analyzed.

[0114] Step S509: Correct the frequency domain space image of the material to be analyzed.

[0115] Step S510: Extract the image information of the corrected frequency domain space image of the material to be analyzed, and in the corrected frequency domain space image of the material to be analyzed, find the peak value and the corresponding coordinates of the diffraction spots included in the corrected frequency domain space image of the material to be analyzed.

[0116] Step S511: For the image pixel points related to the peak position included in the image information, respectively construct fitting curves of the image pixel points in the x direction and the y direction.

[0117] Step S512: Use the fitting curves of each image pixel point in the x direction and the y direction to calculate the extreme point coordinates of each image pixel point, and use the extreme point coordinates to correct the peak position.

[0118] Step S513: Take the center position of the frequency domain space image as the coordinate origin, and translate the pixel points of the corrected peak position.

[0119] Step S514: Generate a coordinate transformation matrix by using the original coordinate values of the peak position and the coordinate values of the peak position in the coordinate system with the center position of the frequency-domain space image as the coordinate origin.

[0120] Step S515: Use the coordinate transformation matrix to perform image reconstruction on the image set of the material to be analyzed.

[0121] The specific implementation processes of the above steps have been described in detail in the above embodiments and will not be elaborated here.

[0122] Furthermore, Figure 6 is a schematic structural diagram of an image reconstruction device provided by an embodiment of the present invention. As Figure 6 shown, the image reconstruction device 600 may include: a calibration unit 601, a coordinate transformation unit 602, and a reconstruction unit 603, where

[0123] The calibration unit 601 is configured to calibrate the frequency-domain space image of the material to be analyzed, where the frequency-domain space image is obtained by performing a Fourier transform on the image set collected for the material to be analyzed in the STEM-EELS mode;

[0124] The matrix construction unit 602 is configured to extract the image information of the calibrated frequency-domain space image and determine the peak position in the frequency-domain space image of the material to be analyzed; generate a coordinate transformation matrix for the image pixel points based on the extracted image information and the peak position;

[0125] The reconstruction unit 603 is configured to use the coordinate transformation matrix to perform image reconstruction on the image set of the material to be analyzed.

[0126] Furthermore, the calibration unit 601 is further configured to perform preliminary noise reduction processing on the image set of the material to be analyzed collected in the STEM-EELS mode; perform a Fourier transform on the preliminarily noise-reduced image to obtain the frequency-domain space image corresponding to the material to be analyzed.

[0127] Furthermore, the calibration unit 601 is further configured to select at least two diffraction spots in the frequency-domain space image, adjust the selected at least two diffraction spots; perform calibration on the frequency-domain space image of the material to be analyzed based on the adjusted diffraction spots.

[0128] Furthermore, the matrix construction unit 602 is further configured to find the peak and the corresponding coordinates of the diffraction spots included in the frequency-domain space image in the frequency-domain space image of the material to be analyzed.

[0129] Further, the matrix construction unit 602 is further configured to respectively construct fitting curves of the image pixel points related to the peak position included in the image information in the x-direction and the y-direction; calculate the extreme point coordinates of each image pixel point by using the fitting curves of each image pixel point in the x-direction and the y-direction, correct the peak position by using the extreme point coordinates; and construct a linear coordinate transformation matrix by using the corrected peak position and its corresponding image information.

[0130] Further, the matrix construction unit 602 is further configured to find the previous pixel point and the next pixel point of the image pixel point in the x-direction, and construct a parabolic curve of the image pixel point in the x-direction by using the previous pixel point and the next pixel point in the x-direction and the pixel value of the image pixel point; find the previous pixel point and the next pixel point of the image pixel point in the y-direction, and construct a parabolic curve of the image pixel point in the y-direction by using the previous pixel point and the next pixel point in the y-direction and the pixel value of the image pixel point.

[0131] Further, the matrix construction unit 602 is further configured to translate the pixel point of the corrected peak position with the center position of the image as the coordinate origin; generate a coordinate transformation matrix by using the original coordinate value of the peak position and the coordinate value of the peak position in the coordinate system with the center position of the image as the coordinate origin.

[0132] It should be noted that the above image reconstruction device can be installed in the existing TEM software in the form of a plug-in, or can be installed as an application on a terminal device or a server.

[0133] Figure 7 An exemplary system architecture 700 to which the transmission electron microscopy image processing method or the transmission electron microscopy image processing device according to the embodiments of the present invention can be applied is shown.

[0134] As Figure 7 shown, the system architecture 700 may include a first terminal device 701 directly connected to the TEM device, a TEM device 702, a network 703, and a second terminal device 704 or a server 705 for transmission electron microscopy image processing. The network 703 is used to provide a medium for communication links between the first terminal device 701 and the TEM device 702, between the TEM device 702 and the second terminal device 704, between the first terminal device 701 and the second terminal device 704, or between the first terminal device 701 and the server 705. The network 703 may include various connection types, such as wired, wireless communication links, or fiber optic cables, etc.

[0135] A user can use the first terminal device 701 to interact with the TEM device 702 via the network 703 to obtain the scanning information of the TEM device 702 or send the control information of the TEM device 702, such as an instruction to control the sample rod to rotate at a constant speed, and an instruction to control the camera to enter the video shooting mode. Software for controlling the TEM device or for displaying the TEM scanning results (only as an example) can be installed on the first terminal device 701.

[0136] The second terminal device 704 or the server 705 is used to obtain image data from the first terminal device 701 and the TEM device 702 respectively, perform image processing or reconstruction on the image data, and store and provide the obtained results to the user.

[0137] The first terminal device 701 and the second terminal device 704 can be various electronic devices with a display screen and supporting web browsing, including but not limited to laptop computers, desktop computers, and the like.

[0138] It should be noted that the image reconstruction method provided by the embodiments of the present invention is generally executed by the second terminal device 704 or the server 705. Correspondingly, the image reconstruction device is generally arranged in the second terminal device 704 or the server 705. In addition, the image reconstruction method can also be completed by the first terminal device 701.

[0139] In addition, the above-mentioned first terminal device 701 and second terminal device 704 may also belong to the same terminal device. Correspondingly, the image reconstruction device is installed on the first terminal device 701 in the form of a plug-in to reconstruct the image data through the image reconstruction method provided by the embodiments of the present invention.

[0140] It should be understood that Figure 7 the number of the second terminal devices or servers in

[0141] is only illustrative. According to the implementation requirements, there can be any number of second terminal devices or servers. Figure 8 Figure 8 The terminal device or server shown is only an example and should not impose any limitations on the functions and usage scope of the embodiments of the present invention.

[0142] Figure 8 As shown in Figure 8As shown, computer system 800 includes a central processing unit (CPU) 801, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 802 or a program loaded from a storage section 808 into a random access memory (RAM) 803. In the RAM 803, various programs and data required for the operation of the system 800 are also stored. The CPU 801, ROM 802, and RAM 803 are connected to each other via a bus 804. An input / output (I / O) interface 805 is also connected to the bus 804.

[0143] The following components are connected to the I / O interface 805: an input section 806 including a keyboard, a mouse, etc.; an output section 807 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc. and a speaker, etc.; a storage section 808 including a hard disk, etc.; and a communication section 809 including a network interface card such as a LAN card, a modem, etc. The communication section 809 performs communication processing via a network such as the Internet. A drive 810 is also connected to the I / O interface 805 as needed. A removable medium 811, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 810 as needed so that a computer program read therefrom can be installed into the storage section 808 as needed.

[0144] Specifically, according to an embodiment disclosed by the present invention, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment disclosed by the present invention includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program contains program codes for performing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 809, and / or installed from the removable medium 811. When the computer program is executed by the central processing unit (CPU) 801, the above functions defined in the system of the present invention are executed.

[0145] It should be noted that the computer-readable medium shown in the present invention can be a computer-readable signal medium, a computer-readable storage medium, or any combination of the above two. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of a computer-readable storage medium can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, a computer-readable storage medium can be any tangible medium that contains or stores a program, and this program can be used by or in combination with an instruction execution system, apparatus, or device. In the present invention, a computer-readable signal medium can include a data signal propagated in a baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, and this computer-readable medium can send, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium can be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0146] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram can represent a module, a program segment, or a part of code, and the above module, program segment, or part of code contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks can occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks shown can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram or flowchart, and the combination of blocks in the block diagram or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0147] The modules involved in the embodiments of the present invention can be implemented in software or in hardware. The described modules can also be provided in a processor. For example, it can be described as: a processor includes a correction unit, a matrix construction unit, and a reconstruction unit. Among them, the names of these modules or units do not constitute a limitation to the module itself in some cases. For example, the correction unit can also be described as "a unit or module for correcting the frequency-domain spatial image of the material to be analyzed".

[0148] As another aspect, the present invention also provides a computer-readable medium. The computer-readable medium can be included in the device described in the above embodiments; or it can exist alone without being assembled into the device. The above computer-readable medium carries one or more programs. When the above one or more programs are executed by a device, the device includes: correcting the frequency-domain spatial image of the material to be analyzed, where the frequency-domain spatial image is obtained by performing a Fourier transform on a set of images collected from the material to be analyzed in the STEM-EELS mode; extracting the image information of the corrected frequency-domain spatial image and determining the peak positions in the frequency-domain spatial image of the material to be analyzed; generating a coordinate transformation matrix for the image pixel points based on the extracted image information and peak positions; and using the coordinate transformation matrix to perform image reconstruction on the set of images of the material to be analyzed.

[0149] According to the technical solution of the embodiments of the present invention, by correcting the frequency-domain spatial image of the material to be analyzed, the corrected frequency-domain spatial image can accurately indicate the feature points and main components of the image of the material to be analyzed through diffraction spots. Generally, the feature points correspond to the peaks in the frequency-domain spatial image. Based on this, by extracting the image information of the corrected frequency-domain spatial image and the peak positions in the frequency-domain spatial image of the material to be analyzed, the positions of the diffraction spots and the image information of the diffraction spots in the frequency-domain spatial image can be preliminarily located. Since the offset directions of the individual pixel points in the set of images are basically the same, subsequently, based on the extracted image information and peak positions, a coordinate transformation matrix is generated for the image pixel points, which can more accurately reflect the transformation of the image pixel points. Then, using the coordinate transformation matrix to perform image reconstruction on the set of images of the material to be analyzed can retain as many image pixel points as possible, effectively improving the resolution and accuracy of the microscopic images of materials with weak radiation resistance or beam-sensitive materials, and facilitating the precise analysis of the local microscopic structure of materials with weak radiation resistance or beam-sensitive materials.

[0150] In addition, the above solution can handle more complex relationships, can transform data through non-linear mapping, so as to capture the complex structure in the data. Through non-linear feature extraction, the microscopic structural features in image data can be revealed more accurately. Especially in complex materials such as molecular sieves, more complex structures and relationships can be identified, providing more accurate analysis results, and can effectively improve the resolution and accuracy of images, avoiding the limitations of processing non-linear data.

[0151] Furthermore, the features obtained by the technical solution provided by the embodiments of the present invention are easier to understand and can be directly associated with physical phenomena (such as the lattice structure of materials, energy loss, etc.). It can directly compare with the actual microscopic structure by extracting the feature points with physical significance in STEM-EELS data, providing higher interpretability and physical connection, which helps to deeply understand and analyze the microscopic structure of materials, especially in the research of materials science, it has more practical application value.

[0152] Furthermore, the technical solution provided by the embodiments of the present invention retains the key features in the STEM-EELS image data and retains the most important structural information in the data. It retains more microscopic structural details by optimizing the data reconstruction process, especially having obvious advantages in features at smaller scales such as pore structures. It provides more accurate analysis, avoids information loss, especially performs excellently in analysis tasks requiring high resolution and high precision, and improves the reliability and accuracy of the structure. In addition, by selecting diffraction spots as feature points, the influence of outliers on the results can be reduced to further improve the reliability and accuracy of the analysis.

[0153] In addition, the technical solution provided by the embodiments of the present invention has a simple data processing process, can significantly improve the calculation efficiency of high-resolution image data, and can meet the requirements of real-time analysis.

[0154] The above specific embodiments do not constitute a limitation to the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations and substitutions can occur depending on design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An image reconstruction method, characterized in that: include: Correcting a frequency domain spatial image of a material to be analyzed, wherein the frequency domain spatial image is obtained by Fourier transforming a set of images of the material to be analyzed collected in a STEM-EELS mode; Extracting image information of the corrected frequency domain spatial image, and determining the peak position in the corrected frequency domain spatial image of the material to be analyzed; Generating a coordinate transformation matrix for image pixels based on the extracted image information and the peak position; The coordinate transformation matrix is ​​used to reconstruct the image set of the material to be analyzed.

2. The image reconstruction method according to claim 1, characterized in that: The image reconstruction method further includes: performing preliminary noise reduction processing on a set of images of the material to be analyzed collected in the STEM-EELS mode; The image after preliminary noise reduction is subjected to Fourier transformation to obtain a frequency domain spatial image corresponding to the material to be analyzed.

3. The image reconstruction method according to claim 1 or 2, characterized in that: The method of correcting the frequency domain spatial image of the material to be analyzed comprises: Selecting at least two diffraction spots in the frequency domain spatial image, and adjusting the selected at least two diffraction spots; Based on the adjusted diffraction spots, the frequency domain spatial image of the material to be analyzed is corrected.

4. The image reconstruction method according to claim 1 or 3, characterized in that: Determining the peak position in the corrected frequency domain spatial image of the material to be analyzed includes: In the corrected frequency domain spatial image of the material to be analyzed, the peak value and the corresponding coordinates of the diffraction spot included in the frequency domain spatial image are searched.

5. The image reconstruction method according to claim 1 or 4, characterized in that: Also includes: For the image pixel points related to the peak position included in the image information, constructing fitting curves of the image pixel points in the x direction and the y direction respectively; Calculating the coordinates of the extreme points in each of the image pixels by using the fitting curves of each of the image pixels in the x-direction and the y-direction, and correcting the peak position by using the extreme point coordinates; The step of generating a coordinate transformation matrix for image pixels includes: The linear coordinate transformation matrix is ​​constructed using the corrected peak position and its corresponding image information.

6. The image reconstruction method according to claim 5, characterized in that: The step of respectively constructing the fitting curves of the image pixels in the x direction and the y direction comprises: Finding a previous pixel point and a next pixel point of the image pixel point in the x direction, and constructing a parabola of the image pixel point in the x direction by using the previous pixel point and the next pixel point in the x direction and the pixel value of the image pixel point; The previous pixel point and the next pixel point of the image pixel point in the y direction are found, and a parabola curve of the image pixel point in the y direction is constructed using the previous pixel point and the next pixel point in the y direction and the pixel value of the image pixel point.

7. The image reconstruction method according to claim 5, characterized in that: The step of constructing a linear coordinate transformation matrix includes: Taking the center position of the frequency domain spatial image as the coordinate origin, the pixel point at the peak position after translation correction; A coordinate transformation matrix is ​​generated by using the original coordinate value of the peak position and the coordinate value of the peak position in a coordinate system with the center position of the frequency domain space image as the coordinate origin.

8. An image reconstruction device, characterized in that: include: A correction unit, a matrix construction unit and a reconstruction unit, wherein: The correction unit is used to correct the frequency domain spatial image of the material to be analyzed, wherein the frequency domain spatial image is obtained by performing Fourier transform on the image set collected by the material to be analyzed in the STEM-EELS mode; The matrix construction unit is used to extract image information of the corrected frequency domain spatial image and determine the peak position in the frequency domain spatial image of the material to be analyzed; based on the extracted image information and the peak position, generate a coordinate transformation matrix for the image pixel points; The reconstruction unit is used to reconstruct the image set of the material to be analyzed by using the coordinate transformation matrix.

9. An electronic device, characterized in that: include: one or more processors; a storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 7.

10. A computer readable medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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