An element migration detection method and system based on image processing

By studying μ-XRF images using image processing techniques and processing element distribution images using Python's OpenCV module, the problems of cumbersome calculations and low accuracy in element migration detection in geology were solved, achieving efficient and accurate element migration detection.

CN115375642BActive Publication Date: 2025-11-18CHINA UNIV OF GEOSCIENCES (BEIJING)
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Patent Information

Application Number
CN202210976029.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-08-15
Publication Date
2025-11-18
Estimated Expiration
2042-08-15

AI Technical Summary

Technical Problem

Existing technologies for calculating element migration in geology involve large computational loads, cumbersome steps, and low accuracy. They are difficult to observe small-scale changes, and different testing methods are used for different samples, leading to errors. Furthermore, the testing costs are high.

Method used

μ-XRF images were studied using image processing techniques. The OpenCV module of Python was used to process the images to obtain the element distribution images, calculate the mass percentage of elements in different endmembers, plot the element change curves and migration rates, and obtain the element correlation and migration diagram results.

Benefits of technology

It improves the accuracy and convenience of element migration detection, avoids a large amount of calculation, enables more detailed observation of element changes, and reduces testing costs.

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Abstract

The application discloses an element migration detection method and system based on image processing. First, a sample to be processed is acquired, a target selection range is obtained after pretreatment of the sample, and a μ-XRF test is performed to obtain an element distribution image of the target selection range; then, the element distribution image is subjected to image processing in a Python OpenCV module to obtain an element migration detection result, including an element change curve and migration rate result, an element correlation result, and an element migration diagram result. The application utilizes image processing technology to process the μ-XRF element distribution image, and the type and degree of the element migration are obtained, which is more convenient than traditional methods, has high accuracy, and can be widely applied.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of image processing, in particular to an element migration detection method and system based on image processing. BACKGROUND

[0002] With the rapid development of computer technology and the continuous improvement of related theories, digital image processing technology has been widely valued and achieved great success in many fields. In geology, a large amount of image data has been accumulated with the maturity of testing technology, but these data cannot be fully utilized by traditional geology, and the information contained therein is difficult to be explored, resulting in a waste of a large amount of image information.

[0003] Most geological processes in nature are accompanied by the migration of various geochemical components (elements) to varying degrees. Accurately defining the types and degrees of geochemical components (elements) that migrate is the premise and key to correctly understanding these geological processes. The existing technology usually uses Gresens equation, Isocon diagram or standardized Isocon diagram mass balance method to calculate the whole rock major and trace data of different end-member samples to study the migration rules of components (elements) at different stages.

[0004] Then, the mass balance method is used to calculate the whole rock major and trace data, which has the following disadvantages: large amount of calculation; complicated calculation steps; the element content range needs to be limited according to experience when plotting; the overall change is reflected, which is rough and not fine, and it is not easy to observe the change of small-scale elements; the sample selection needs to be typical and uniform; there is no unified testing method, different samples are processed by different testing methods, which produces errors; the sample requirements are strict when sending; the testing cost is expensive.

[0005] In geology, a large amount of image data has been accumulated with the maturity of testing technology, but these data cannot be fully utilized by traditional geology, and the information contained therein is difficult to be explored, resulting in a waste of a large amount of image information. In this background, image processing technology urgently needs to be applied to the field of geological science. SUMMARY

[0006] Therefore, the embodiments of the present application provide an element migration detection method and system based on image processing, which studies μ-XRF images by using image processing technology, avoids a large amount of calculation process compared to the existing element migration detection method, has higher accuracy, and can be universally applied.

[0007] In a first aspect, an element migration detection method based on image processing is provided, the method comprising:

[0008] The sample to be processed is acquired, the sample is preprocessed to obtain the target selection range, and μ-XRF testing is performed to obtain the elemental distribution image of the target selection range; wherein, the preprocessing includes selecting the scanning range of the sample and dividing endmembers;

[0009] The element distribution image is processed using Python's OpenCV module to obtain element migration detection results;

[0010] The element distribution image is processed using Python's OpenCV module, including:

[0011] Get the pixel percentage of each end-member, and combine it with the element quality percentage to obtain the quality percentage of each element in each end-member;

[0012] The element change curves, migration rate results, element correlation results, and element migration diagram results were obtained based on the mass percentage of elements in different endmembers.

[0013] Optionally, obtaining the pixel percentage of each endmember and combining it with the element quality percentage to obtain the quality percentage of each element in each endmember includes:

[0014] Read the height and width channels of the element distribution image, convert the image to grayscale, and obtain the total pixel count a;

[0015] Traverse the elements according to the migration direction, and combine the preset step size to extract different endmembers to obtain the total number of pixels b in different endmember regions, and calculate the percentage i of each endmember pixel, where i = b / a;

[0016] Combined with μ-XRF, the corresponding elemental mass percentage m is obtained. x Calculate the mass percentage w of the corresponding element x in different endmembers. x , where w x =i x *m x .

[0017] Optionally, obtaining the elemental variation curve and mobility results based on the mass percentage of elements in different endmembers includes:

[0018] Based on the width and height step size of the end element, the statistical data of each end element is matched with the element.

[0019] Initialize the element distribution plot, wherein the horizontal axis step size of the element distribution plot is the position of different endmembers, and the vertical axis is the statistical value;

[0020] Plotting is performed based on the statistical data of each endpoint, and the overall plotting result and the plotting results of each element are saved to obtain the element change curve; when plotting the overall plot, the element with the smallest degree of change is selected as the inactive element;

[0021] The element mobility rate is calculated based on the first formula to obtain the degree of element migration. The first formula specifically includes:

[0022]

[0023] μ represents the elemental mobility, w x w represents the mass percentage of the corresponding element x in different endmembers. 原始 This indicates the percentage of the corresponding element's mass in the initial endmember.

[0024] Optionally, obtaining the element correlation result based on the mass percentage of elements in different endmembers includes:

[0025] Use the statistical data of the selected elements as the horizontal axis and the statistical data of the non-selected elements as the vertical axis to draw an element correlation diagram.

[0026] Based on the element correlation map, the fitting curve and fitting coefficient values ​​of the inter-element correlation are obtained, and the fitting curve and fitting coefficient values ​​are used to characterize the element correlation results.

[0027] Optionally, obtaining the element migration diagram result based on the mass percentage of elements in different endmembers includes:

[0028] An element migration diagram is drawn by using the statistical data of each element in the original endmember as the horizontal axis and the statistical data of each element in the selected endmember as the vertical axis. The statistical data of each element is automatically scaled by Python. The element migration diagram is used to represent the result of the element migration diagram.

[0029] Secondly, an image processing-based element migration detection system is provided, the system comprising:

[0030] The testing module is used to acquire the sample to be processed, preprocess the sample to obtain the target selection range, and perform μ-XRF testing to obtain the elemental distribution image of the target selection range; wherein, the preprocessing includes selecting the scanning range of the sample and dividing endmembers;

[0031] The processing module is used to perform image processing on the element distribution image using Python's OpenCV module to obtain element migration detection results;

[0032] The element distribution image is processed using Python's OpenCV module, including:

[0033] Get the pixel percentage of each end-member, and combine it with the element quality percentage to obtain the quality percentage of each element in each end-member;

[0034] The element change curves, migration rate results, element correlation results, and element migration diagram results were obtained based on the mass percentage of elements in different endmembers.

[0035] Optionally, the processing module obtains the pixel percentage of each endmember and combines it with the element quality percentage to obtain the quality percentage of each element in each endmember, including:

[0036] Read the height and width channels of the element distribution image, convert the image to grayscale, and obtain the total pixel count a;

[0037] Traverse the elements according to the migration direction, and combine the preset step size to extract different endmembers to obtain the total number of pixels b in different endmember regions, and calculate the percentage i of each endmember pixel, where i = b / a;

[0038] Combined with μ-XRF, the corresponding elemental mass percentage m is obtained. x Calculate the mass percentage w of the corresponding element x in different endmembers. x , where w x =i x *m x .

[0039] Optionally, the processing module obtains element change curves and mobility results based on the mass percentage of elements in different endmembers, including:

[0040] Based on the width and height step size of the end element, the statistical data of each end element is matched with the element.

[0041] Initialize the element distribution plot, wherein the horizontal axis step size of the element distribution plot is the position of different endmembers, and the vertical axis is the statistical value;

[0042] Plotting is performed based on the statistical data of each endpoint, and the overall plotting result and the plotting results of each element are saved to obtain the element change curve; when plotting the overall plot, the element with the smallest degree of change is selected as the inactive element;

[0043] The element mobility rate is calculated based on the first formula to obtain the degree of element migration. The first formula specifically includes:

[0044]

[0045] μ represents the elemental mobility, w x w represents the mass percentage of the corresponding element x in different endmembers. 原始 This indicates the percentage of the corresponding element's mass in the initial endmember.

[0046] Optionally, the processing module obtains element correlation results based on the quality percentage of elements in different endmembers, including:

[0047] Use the statistical data of the selected elements as the horizontal axis and the statistical data of the non-selected elements as the vertical axis to draw an element correlation diagram.

[0048] Based on the element correlation map, the fitting curve and fitting coefficient values ​​of the inter-element correlation are obtained, and the fitting curve and fitting coefficient values ​​are used to characterize the element correlation results.

[0049] Optionally, the processing module obtains element migration diagram results based on the quality percentage of elements in different endmembers, including:

[0050] An element migration diagram is drawn by using the statistical data of each element in the original endmember as the horizontal axis and the statistical data of each element in the selected endmember as the vertical axis. The statistical data of each element is automatically scaled by Python. The element migration diagram is used to represent the result of the element migration diagram.

[0051] The technical solution provided in this application first obtains the sample to be processed, preprocesses the sample to obtain the target selection range, and performs μ-XRF testing to obtain the element distribution image of the target selection range. The preprocessing includes selecting a scanning range for the sample and dividing it into endmembers. Then, the element distribution image is processed using Python's OpenCV module to obtain element migration detection results. The pixel percentage of each endmember is obtained, and combined with the element mass percentage, the mass percentage of each element in each endmember is obtained. Based on the mass percentage of elements in different endmembers, element change curves, migration rate results, element correlation results, and element migration diagram results are obtained. It can be seen that the beneficial effect of this invention is that it utilizes image processing technology to process μ-XRF element distribution images to obtain the types and degrees of element migration, which is more convenient and accurate than traditional methods and can be widely applied. Attached Figure Description

[0052] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0053] Figure 1 A flowchart of an element migration detection step based on image processing is provided in an embodiment of this application;

[0054] Figure 2 A flowchart of an element migration detection based on image processing is provided as an optional embodiment of this application;

[0055] Figure 3This is a block diagram of an element migration detection system based on image processing, provided as an embodiment of this application. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0057] In the description of this invention, the terms “comprising,” “having,” and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units that are expressly listed, but may also include other steps or units that are not expressly listed but are inherent to these processes, methods, products, or apparatuses, or steps or units added based on further optimizations of the inventive concept.

[0058] This application utilizes image processing techniques to study the element migration patterns in μ-XRF images. μ-XRF testing can obtain element distribution maps at both large and very fine scales. By extracting feature information using Python's image processing techniques, the pixel matrix of element distribution, the change curves and migration rates of different elements at different stages, and the correlation between elements can be obtained. Compared with traditional methods, this avoids a large amount of computation, has higher accuracy, and can be widely applied. For details, please refer to... Figure 1 The diagram illustrates a flowchart of an image processing-based element migration detection method provided in an embodiment of this application. The method may include the following steps:

[0059] Step 101: Obtain the sample to be processed, preprocess the sample to obtain the target selection range, and perform μ-XRF testing to obtain the element distribution image of the target selection range.

[0060] The preprocessing includes selecting the scanning range of the sample and dividing it into endmembers.

[0061] In this embodiment, samples and elements are first selected, the scanning range of the samples is selected and the endmembers are divided, and μ-XRF testing is performed to obtain the element distribution image of the selected range;

[0062] Step 102: Perform image processing on the element distribution image using Python's OpenCV module to obtain element migration detection results.

[0063] The element distribution image is processed in Python's OpenCV module, including obtaining the pixel percentage of each endmember, combining it with the element quality percentage to obtain the quality percentage of each element in each endmember; and obtaining the element change curve and migration rate results, element correlation results, and element migration diagram results based on the quality percentage of elements in different endmembers.

[0064] In the embodiments of this application, such as Figure 2 Step 102 involves image processing of the μ-XRF image using Python's OpenCV module, specifically including:

[0065] (1) Obtain the pixel distribution map of the element. Input the image path and height / width stride, read the image to obtain the height and width channels, convert the image to grayscale, obtain the total pixel sum 'a', combine with real geological facts, traverse according to the element migration direction, combine with the stride to truncate different endmembers, obtain the total pixel sum 'b' of different endmember regions, save it to the corresponding matrix grid, and calculate the percentage i of each endmember pixel, which represents the percentage of the element in each endmember. Combine with the corresponding element x mass percentage m obtained by μ-XRF. x Calculate the mass percentage w of the corresponding element x in different endmembers. x .

[0066] i = b / a

[0067] w x =i x *m x

[0068] (2) Obtain element change curves and migration rates. Set the image path and set the width and height step size according to the endmembers. Match the statistical data of each endmember with the elements, initialize the element distribution plot, with the horizontal axis step size representing the different endmember positions and the vertical axis representing the statistical values. Save the overall plotting results and the plotting results of individual elements, and automatically calculate the element migration rate to obtain the degree of element migration. When plotting the overall plot, select the element with the smallest degree of change as the inactive element.

[0069] The element mobility rate is calculated using the first formula to obtain the degree of element migration. The first formula specifically includes:

[0070]

[0071] μ represents the elemental mobility, w x w represents the mass percentage of the corresponding element x in different endmembers. 原始 This indicates the percentage of the corresponding element's mass in the initial endmember.

[0072] (3) Obtain the correlation between elements. Plot the correlation diagram with the statistical data of the selected element as the horizontal axis and the statistical data of other elements as the vertical axis. Obtain the changes of other elements as the content of the selected element increases, and obtain the fitting curve of the correlation between elements and the fitting coefficient value. Then, the changes of minerals can be inferred by combining geological facts.

[0073] (4) Obtain the element migration diagram. Plot the element migration diagram with the original end-member element statistics as the horizontal axis and the selected end-member element statistics as the vertical axis. Python is set to automatically scale the element statistics.

[0074] like Figure 3 This application also provides an element migration detection system 300 based on image processing. System 300 includes:

[0075] The test module 301 is used to acquire the sample to be processed, preprocess the sample to obtain the target selection range, and perform μ-XRF testing to obtain the elemental distribution image of the target selection range; wherein, the preprocessing includes selecting the scanning range of the sample and dividing the endmembers;

[0076] The processing module 302 is used to perform image processing on the element distribution image in the Python OpenCV module to obtain element migration detection results. The image processing on the element distribution image in the Python OpenCV module includes obtaining the pixel percentage of each endmember, combining it with the element quality percentage to obtain the quality percentage of each element in each endmember, and obtaining the element change curve and migration rate results, element correlation results, and element migration diagram results based on the quality percentage of the element in different endmembers.

[0077] In an optional embodiment of this application, the processing module 302 obtains the pixel percentage of each end-member and combines it with the element quality percentage to obtain the quality percentage of each element in each end-member, including:

[0078] Read the height and width channels of the element distribution image, convert the image to grayscale, and obtain the total pixel count 'a'.

[0079] Traverse the elements according to the migration direction, and combine the preset step size to extract different endmembers to obtain the total number of pixels b in different endmember regions, and calculate the percentage i of each endmember pixel, where i = b / a;

[0080] Combined with μ-XRF, the corresponding elemental mass percentage m is obtained. x Calculate the mass percentage w of the corresponding element x in different endmembers. x , where w x =i x *m x .

[0081] In an optional embodiment of this application, the processing module 302 obtains the element change curve and mobility results based on the mass percentage of elements in different endmembers, including:

[0082] Based on the width and height step size of the end element, the statistical data of each end element is matched with the element.

[0083] Initialize the element distribution plot, where the step size of the horizontal axis in the element distribution plot is the position of different endmembers, and the vertical axis is the statistical value;

[0084] Plotting is performed based on the statistical data of each endpoint, and the overall plotting result and the plotting results of each element are saved to obtain the element change curve; when plotting the overall plot, the element with the smallest degree of change is selected as the inactive element;

[0085] The element mobility rate is calculated based on the first formula to obtain the degree of element migration. The first formula specifically includes:

[0086]

[0087] μ represents the elemental mobility, w x w represents the mass percentage of the corresponding element x in different endmembers. 原始 This indicates the percentage of the corresponding element's mass in the initial endmember.

[0088] In an optional embodiment of this application, the processing module 302 obtains element correlation results based on the quality percentage of elements in different endmembers, including:

[0089] Use the statistical data of the selected elements as the horizontal axis and the statistical data of the non-selected elements as the vertical axis to draw an element correlation diagram.

[0090] Based on the element correlation map, the fitting curve and fitting coefficient values ​​of the inter-element correlation are obtained. The fitting curve and fitting coefficient values ​​are used to characterize the element correlation results.

[0091] In an optional embodiment of this application, the processing module 302 obtains element migration diagram results based on the mass percentage of elements in different endmembers, including:

[0092] An element migration diagram is drawn by using the statistical data of each element in the original endmember as the x-axis and the statistical data of each element in the selected endmember as the y-axis. The statistical data of each element is automatically scaled by Python. The element migration diagram is used to represent the result of the element migration diagram.

[0093] The image processing-based element migration detection system provided in this application is used to implement the image processing-based element migration detection method described above. Specific limitations of the image processing-based element migration detection system can be found in the limitations of the image processing-based element migration detection method described above, and will not be repeated here. Each part of the image processing-based element migration detection system can be implemented entirely or partially through software, hardware, or a combination thereof. The modules can be embedded in or independent of the processor in the device, or stored in the device's memory in software form, so that the processor can call and execute the operations corresponding to each module.

[0094] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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.

[0095] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. An element migration detection method based on image processing, characterized in that, The method includes: A sample to be processed is acquired, and the sample is preprocessed to obtain the target selection range. Then, μ-XRF testing is performed to obtain the elemental distribution image of the target selection range. The preprocessing includes selecting a scanning range for the sample and dividing it into endmembers. The element distribution image is processed using Python's OpenCV module to obtain element migration detection results; The element distribution image is processed using Python's OpenCV module, including: Get the pixel percentage of each end-member, and combine it with the element quality percentage to obtain the quality percentage of each element in each end-member; Based on the mass percentage of elements in different endmembers, we obtained element change curves and mobility results, element correlation results, and element migration diagram results. Obtain the pixel percentage of each endmember, and combine it with the element quality percentage to obtain the overall quality percentage of each element in each endmember, including: Read the height and width channels of the element distribution image, convert the image to grayscale, and obtain the total pixel count a; Traverse the elements according to the migration direction, and combine the preset step size to extract different endmembers to obtain the total number of pixels b in different endmember regions, and calculate the percentage i of each endmember pixel, where i = b / a; Combined with μ-XRF, the corresponding elemental mass percentage m is obtained. x Calculate the mass percentage w of the corresponding element x in different endmembers. x , where w x =i x *m x ; Elemental variation curves and mobility results were obtained based on the mass percentage of elements in different endmembers, including: Based on the width and height step size of the end element, the statistical data of each end element is matched with the element. Initialize the element distribution plot, wherein the horizontal axis step size of the element distribution plot is the position of different endmembers, and the vertical axis is the statistical value; Plotting is performed based on the statistical data of each endpoint, and the overall plotting result and the plotting results of each element are saved to obtain the element change curve; when plotting the overall plot, the element with the smallest degree of change is selected as the inactive element; The element mobility rate is calculated based on the first formula to obtain the degree of element migration. The first formula specifically includes: μ represents the elemental mobility, w x w represents the percentage of the mass of the corresponding element x in different endmembers. 原始 This indicates the percentage of the corresponding element's mass in the initial endmember.

2. The method according to claim 1, characterized in that, The method of obtaining element correlation results based on the mass percentage of elements in different endmembers includes: Use the statistical data of the selected elements as the horizontal axis and the statistical data of the non-selected elements as the vertical axis to draw an element correlation diagram. Based on the element correlation map, the fitting curve and fitting coefficient values ​​of the inter-element correlation are obtained, and the fitting curve and fitting coefficient values ​​are used to characterize the element correlation results.

3. The method according to claim 1, characterized in that, The element migration diagram results obtained based on the mass percentage of elements in different endmembers include: An element migration diagram is drawn by using the statistical data of each element in the original endmember as the horizontal axis and the statistical data of each element in the selected endmember as the vertical axis. The statistical data of each element is automatically scaled by Python. The element migration diagram is used to represent the result of the element migration diagram.

4. An element migration detection system based on image processing, characterized in that, The system includes: The testing module is used to acquire the sample to be processed, preprocess the sample to obtain the target selection range, and perform μ-XRF testing to obtain the elemental distribution image of the target selection range; wherein, the preprocessing includes selecting the scanning range of the sample and dividing endmembers; The processing module is used to perform image processing on the element distribution image using Python's OpenCV module to obtain element migration detection results; The element distribution image is processed using Python's OpenCV module, including: Get the pixel percentage of each end-member, and combine it with the element quality percentage to obtain the quality percentage of each element in each end-member; Based on the mass percentage of elements in different endmembers, we obtained element change curves and mobility results, element correlation results, and element migration diagram results. The processing module obtains the pixel percentage of each endmember and combines it with the element quality percentage to obtain the overall quality percentage of each element in each endmember, including: Read the height and width channels of the element distribution image, convert the image to grayscale, and obtain the total pixel count a; Traverse the elements according to the migration direction, and combine the preset step size to extract different endmembers to obtain the total number of pixels b in different endmember regions, and calculate the percentage i of each endmember pixel, where i = b / a; Combined with μ-XRF, the corresponding elemental mass percentage m is obtained. x Calculate the mass percentage w of the corresponding element x in different endmembers. x , where w x =i x *m x ; The processing module obtains elemental variation curves and mobility results based on the mass percentage of elements in different endmembers, including: Based on the width and height step size of the end element, the statistical data of each end element is matched with the element. Initialize the element distribution plot, wherein the horizontal axis step size of the element distribution plot is the position of different endmembers, and the vertical axis is the statistical value; Plotting is performed based on the statistical data of each endpoint, and the overall plotting result and the plotting results of each element are saved to obtain the element change curve; when plotting the overall plot, the element with the smallest degree of change is selected as the inactive element; The element mobility rate is calculated based on the first formula to obtain the degree of element migration. The first formula specifically includes: μ represents the elemental mobility, w x w represents the mass percentage of the corresponding element x in different endmembers. 原始 This indicates the percentage of the corresponding element's mass in the initial endmember.

5. The system according to claim 4, characterized in that, The processing module obtains element correlation results based on the quality percentage of elements in different endmembers, including: Use the statistical data of the selected elements as the horizontal axis and the statistical data of the non-selected elements as the vertical axis to draw an element correlation diagram. Based on the element correlation map, the fitting curve and fitting coefficient values ​​of the inter-element correlation are obtained, and the fitting curve and fitting coefficient values ​​are used to characterize the element correlation results.

6. The system according to claim 4, characterized in that, The processing module obtains element migration diagram results based on the quality percentage of elements in different endmembers, including: An element migration diagram is drawn by using the statistical data of each element in the original endmember as the horizontal axis and the statistical data of each element in the selected endmember as the vertical axis. The statistical data of each element is automatically scaled by Python. The element migration diagram is used to represent the result of the element migration diagram.

Citation Information

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