A 2D wadell roundness calculation method of zircon image based on curvature

Abstract

The application discloses a kind of 2D Wadell roundness calculation methods of zircon image based on curvature, comprising:1, obtain zircon picture and detect zircon contour, calculate the maximum inscribed circle radius of contour, utilize cyclic pseudo roundness determination method to successively carry out interpolation and smoothing processing to zircon contour,2, the concave and convex of point on contour is judged using vector cross product method, retain the convex arc segment in it as the angle of contour,3, after the point with curvature radius greater than the maximum inscribed circle radius in angle is deleted, further angle operation is carried out to the remaining point of angle using SC method,4, the angle circle that is in accord with 2D Wadell roundness definition and is inlaid in angle is found using re-fitting method, finally calculate 2D Wadell roundness.The 2D Wadell roundness of profile can be detected quickly and accurately by the application, reduce the labor cost of the previous need for manual drawing of angle circle, and can improve detection efficiency, is conducive to carrying out relevant resource environment work.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of material science and mineralogy, and particularly relates to a 2D Wadell roundness calculation method of zircon image based on curvature. BACKGROUND

[0002] The shape of particulate material has an impact on many engineering and technical fields, and calculating the shape parameters of mineral particles helps to understand important information about the deposition environment, geological history and formation process of the particles. Among them, 2D Wadell roundness is a widely used index to describe the relative sharpness of particle angles. In the traditional calculation of 2D Wadell roundness of zircon, researchers need to manually compare the curvature radius of each angle of zircon particles with the curvature radius of the round hole size under the condition that the computer hardware performance is not developed. This measurement method is highly dependent on manpower and very low in efficiency. Even if the single zircon particle roundness calibration calculation is completed, it also needs a high time cost.

[0003] Currently, the two-dimensional contour information of particles can be obtained by digital image processing and three-dimensional scanning method, 2D Wadell roundness calculation can be performed, and the curvature radius can be estimated by fitting an angle circle at the round corner. The biggest advantage of digital image processing is low cost, easy to collect and small data volume. The obtained particle contour is representative, and very fine particles (such as rock thin sections) can be imaged by a microscope.

[0004] However, since the essence of digital image is a pixel matrix, the particle contour obtained from the image inevitably has jagged edges - this is a small range of random error, which usually has no clear direction and fluctuates around the true value. However, 2D Wadell roundness is highly sensitive to the jagged edges around the particle contour. Since the calculation of the curvature radius depends on the overall smoothness of the identified scale, the presence of jagged edges will cause significant fluctuations in the curvature. If the jagged edges are not removed, it is possible to identify the edges as particle angles.

[0005] Therefore, based on the above reasons, Reference 1: Vangla, P., Roy, N. & Gali, ML Image basedshape characterization of granular materials and its effect on kinematics of particle motion. Granul. Matter. 20(1), 6. https: / / doi.org / 10.1007 / s10035-017-0776-8 (2017) uses image fast Fourier transform and linear polygon approximation to denoise particle contours, with significant smoothing effect. Reference 2: Isik, H. & Cabalar, AF A shape parameter for soil particles using a computational method. Arab. J. Geosci. 15(7), 581. https: / / doi.org / 10.1007 / s12517-022-09777-x (2022) The particle contours are transformed to the frequency domain using Fourier transform to obtain smooth particle contours, as shown in reference 3: Chen, J., Zhang, Z., Lin, D., Li, L., & Xu, W. (2024). An improved corner dealiasing and recognition algorithm for 2D Wadell roundness computation. Scientific Reports, 14(1), 9439. A cyclic median filtering method is used to denoise the contours, and a line graph showing the corresponding number of iterations and error range is provided. However, these methods struggle to balance the smoothness and non-deformation of the particle contours during denoising. Furthermore, methods that transform particle contours to the frequency domain suffer from low computational efficiency when fitting details, difficulty in fitting sharp corners, and generally blunt results. Summary of the Invention

[0006] To address the shortcomings of the existing technology, this invention proposes a 2D Wadell roundness calculation method based on curvature zircon images. This method aims to quickly and accurately detect the 2D Wadell roundness of the contour, reduce the labor cost of manually drawing corner rounds, and improve detection efficiency. It can be applied to particle shape quantification research in multiple related fields.

[0007] The present invention adopts the following technical solution to solve the technical problem:

[0008] The 2D Wadell sphericity calculation method for zircon image based on curvature has the characteristics that it comprises the following steps:

[0009] Step 1, acquire a zircon image and detect the contour of a zircon grain in the image, and perform interpolation and smoothing processing on the contour of the zircon grain in sequence by using a cyclic pseudo-sphericity determination method to obtain a pre-processed contour of the zircon grain;

[0010] Step 2, determine the concave-convex property of the pre-processed contour by using a vector cross product method, and retain the convex arc segments therein as angles of the contour;

[0011] Step 3, delete the contour points in each angle with a curvature radius greater than , and perform angle division on the remaining contour points in each angle by using an abnormal curvature angle division method to obtain a normal angle set;

[0012] Step 4, find an angle circle that is inscribed in the normal angles and meets the 2D Wadell sphericity by using a re-fitting method, so as to calculate the 2D Wadell sphericity .

[0013] The 2D Wadell sphericity calculation method for zircon image based on curvature has the characteristics that the step 1 comprises the following steps:

[0014] Step 1.1, acquire a zircon image and extract the contour of a zircon grain in the image, and obtain the contour of the zircon grain , and calculate the maximum inscribed circle radius of the contour ; wherein, represents the i-th contour point, and M represents the total number of contour points of the zircon grain; Let the coordinates of

[0015] be ;

[0016] Step 1.2, obtain the curvature of the i-th contour point of the contour of the zircon grain by using formula (1), so as to take the reciprocal of as the curvature radius of the i-th contour point ;

[0017] (1)

[0018] Step 1.3, calculate the pseudo-sphericity of the contour of the zircon grain by using formula (2): ​​​

[0019] (2)

[0020] Step 1.4, calculating the Euclidean distance between any two adjacent contour points in the contour of the zircon particle, thereby obtaining a set of Euclidean distances , wherein, denotes the Euclidean distance between the contour point and the contour point ;

[0021] Step 1.5, calculating the number of interpolation points by using formula (3) :

[0022] (3)

[0023] In formula (3), denotes the mode, and is the symbol of rounding up; denotes the threshold value, and the value range is ;

[0024] Step 1.6, calculating the variance of , when is greater than 3× , performing linear interpolation between and times, thereby obtaining the interpolated contour; Step 1.7, performing Gaussian filtering smoothing on the interpolated contour for

[0025] times, and then calculating the pseudo-circularity of the smoothed contour ;

[0026] Step 1.8, if the difference between the pseudo-circularities is greater than a given threshold value , then the smoothed contour is sequentially executed in step 1.2, otherwise, the smoothed contour is taken as the pre-processed contour of the zircon particle, and the process goes to step 2. Further, the step 2 includes the following steps:

[0027] Step 2.1, traversing the contour points in the pre-processed contour, finding a contour point set with the maximum vertical coordinate

[0028] , and finding a contour point with the maximum horizontal coordinate from the contour point set , calculating the vector composed of the contour point and the previous adjacent point ; ​​​​​and outline points With the next adjacent point The vector formed Cross product between ;

[0029] Step 2.2: For the preprocessed contour... Contour points ,calculate and the previous adjacent point The vector formed as well as Contour of the next adjacent point The vector formed Cross product between ;

[0030] Step 2.3, if If less than 0, it means the first... Contour points If it belongs to a convex arc segment, otherwise, delete the first segment from the preprocessed contour. Contour points Thus, the remaining outline is obtained;

[0031] Step 2.4: Cluster the contour points in the remaining contours whose index values ​​differ by 1 into one class, and each class corresponds to a corner on the contour.

[0032] Furthermore, step 3 includes the following steps:

[0033] Step 3.1: Calculate the radius of curvature of each contour point at any corner, and set the radius of curvature greater than 1. Delete the outline points to obtain the remaining angles;

[0034] Step 3.2: Determine whether the contour point corresponding to the maximum radius of curvature of each point in the remaining angle is located on the boundary of its own angle; if yes, proceed to step 3.3; otherwise, proceed to step 3.5.

[0035] Step 3.3: Determine whether the quotient of the maximum radius of curvature divided by the minimum radius of curvature at each point in the remaining angle is greater than... If yes, delete the contour point with the maximum radius of curvature in the corresponding angle and return to step 3.3; otherwise, treat the corresponding angle as a normal angle and add it to the normal angle set.

[0036] Step 3.4: Determine whether the number of contour points of each angle in the normal angle set is less than 3. If so, delete the corresponding angle; otherwise, leave it unchanged to obtain the final normal angle set and proceed to step 4.

[0037] Step 3.5: Obtain the contour point index corresponding to the maximum radius of curvature. and the index is taken as the center of the angle circle, and the step 3.2 is executed sequentially.

[0038] Further, the step 4 includes the following steps:

[0039] Step 4.1, the first derivative of the curvature radius of each contour point on any normal angle is calculated, and each contour point on the normal angle is sorted in ascending order according to the absolute value of the first derivative to obtain a sorted angle point sequence ;

[0040] Step 4.2, the curvature center of the first point of the angle point sequence is calculated by formula (4) and taken as the center of the angle circle:

[0041] (4)

[0042] In formula (4), and respectively represent the first derivative of and , and represents the curvature at the point ;

[0043] Step 4.3, the curvature radius of the first point of the angle point sequence is calculated and taken as the radius of the angle circle;

[0044] Step 4.4, according to the center and radius of the angle circle, it is judged whether the angle circle is within the contour of the zircon particle , if yes, the corresponding angle circle is added to the angle circle set ; otherwise, the first point is deleted from and the step 4.2 is executed sequentially to obtain the final angle circle set ;

[0045] Step 4.5, the final roundness of the zircon particles in the zircon image is calculated by formula (5):

[0046] (5)

[0047] In formula (5), represents the radius of the s-th angle circle in the final angle circle set , and N represents the total number of angle circles in the final angle circle set . ​​

[0048] The electronic device of the present application comprises a memory and a processor, and is characterized in that the memory is used to store a program supporting the processor to execute the 2D Wadell roundness method for calculating the digital image of zircon particles, and the processor is configured to execute the program stored in the memory.

[0049] The computer readable storage medium of the present application has a computer program stored thereon, and is characterized in that the computer program, when executed by a processor, performs the steps of the 2D Wadell roundness method for calculating the digital image of zircon particles.

[0050] Compared with the prior art, the present application has the following beneficial effects:

[0051] 1. The present application proposes a cyclic pseudo-roundness determination method for interpolating and smoothing the contour of zircon, which can obtain a contour that retains the original shape of the zircon particles without manual determination of the number of cyclic smoothing times, and improves the calculation efficiency of the 2D Wadell roundness of zircon without loss of accuracy.

[0052] 2. The present application proposes a vector cross product method to determine the concave-convex nature of points on the contour, which can accurately identify the convex arc segment in the smoothed contour as a contour angle while simplifying the calculation, thereby providing a new scientific and reasonable solution for angle identification.

[0053] 3. The abnormal curvature angle division method proposed by the present application can effectively identify two angles that are difficult to identify due to being too close, improve the 2D Wadell roundness accuracy of zircon particles, and further help to reduce the subtle errors in the calibration process, achieving a balance between maintaining accuracy and reducing sawtooth noise.

[0054] 4. The re-fitting method proposed by the present application can accurately fit the angle circle that meets the 2D Wadell definition in the case of angle tip ambiguity due to a relatively blunt angle, and compared with the least square fitting method used in the previous method, it can find the true angle circle that is tangent to the angle, thereby alleviating the problem of large roundness calculation results caused by the least square method. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 The flowchart of the method of the present application;

[0056] Figure 2 The visualization result graph of the practical application of the method of the present application. DETAILED DESCRIPTION

[0057] In the embodiment, when geological engineering is carried out, the 2D Wadell sphericity calculation method for zircon image based on curvature can be used to quickly and conveniently calibrate the sphericity of zircon, so as to judge the transport time, transport distance, formation history and mechanical action type in the formation process of zircon; in the study of hydraulic fracturing, the special hydraulic fracturing sand without sharp corners can be screened in large quantities; in macro and micro geotechnical engineering, the micro morphology characteristics of natural sand can be accurately quantitatively evaluated, and the mechanical properties and application scenarios are judged. In actual operation, compared with the previous method, the cyclic pseudo-sphericity determination method used in the application can maintain the shape of zircon without artificial adjustment of the number of smoothing times, and the calculation accuracy is not sacrificed. The vector cross product method and abnormal curvature angle division method are used to efficiently and accurately identify all angles in the contour, and the re-fitting method is used to avoid the sphericity bluntness problem caused by the least square fitting to a certain extent. Specifically, as shown in Figure 1 , the method comprises the following steps:

[0058] Step 1, acquiring a zircon image and detecting the contour of the zircon particle in the image, and using a cyclic pseudo-sphericity determination method to sequentially perform interpolation and smoothing processing on the contour of the zircon particle:

[0059] Step 1.1, acquiring a zircon image, using an image segmentation large model FastSAM to identify the foreground object zircon in the picture, applying a binary mask to the zircon, and then extracting the contour of the zircon particle by using an image topology analysis algorithm proposed by Satoshi Suzuki in 1985 , wherein, represents the th contour point, M represents the total number of contour points of the zircon particle, the nearest distance map of each point in the zircon particle to the contour is calculated, the center of the maximum inscribed circle is the point farthest from the internal contour of the particle, and the maximum distance in the distance map is the maximum inscribed circle radius of the contour ;

[0060] Let the coordinates of be .

[0061] Step 1.2, the curvature of the th contour point of the zircon particle is obtained by using formula (1), so that the reciprocal of is taken as the curvature radius of the th contour point ;

[0062] (1)

[0063] Step 1.3: Calculate the pseudo-roundness of the zircon grain profile using equation (2). :

[0064] (2)

[0065] Step 1.4: Calculate the Euclidean distance between any two adjacent points in the profile of the zircon grain, thus obtaining the set of Euclidean distances. ,in, Indicates the first Contour points and the Contour points The Euclidean distance.

[0066] Step 1.5: Calculate the number of interpolation points using equation (3). :

[0067] (3)

[0068] In equation (3), Indicates taking the mode. It is the symbol for rounding up; This represents the threshold value, and its range is [value range missing]. ;

[0069] Step 1.6, Calculation variance ,according to In principle, when Greater than 3× This indicates the distance. Abnormalities, then in and Between Linear interpolation is used to obtain the interpolated contour.

[0070] Step 1.7: Perform interpolation on the contour. After smoothing with a second-Gaussian filter, the pseudo-circularity of the smoothed contour is then calculated. ;

[0071] Step 1.8, if the difference in pseudo-roundness Greater than a given threshold If there are still jagged noises on the contour that have not been eliminated, then the smoothed contour will be carried into step 1.2 and executed sequentially; otherwise, the smoothed contour will be used as the pre-processed contour of the zircon particles, and the process will proceed to step 2.

[0072] Step 2: Use the vector cross product method to determine the concavity / convexity of the preprocessed contour, and retain the convex arc segments as the contour angles:

[0073] Step 2.1: Traverse the contour points in the preprocessed contour and find the set of contour points whose ordinates have the maximum values. and from the contour point set Find the contour point with the largest x-coordinate Calculate contour points Adjacent to the previous point The vector formed and outline points With the next adjacent point The vector formed Cross product between ;

[0074] Step 2.2: For the preprocessed contour... Contour points ,calculate and the previous adjacent point The vector formed as well as Contour of the next adjacent point The vector formed Cross product between ;

[0075] Step 2.3, if If less than 0, it means the first... Contour points If it belongs to a convex arc segment, otherwise, delete the first segment from the preprocessed contour. Contour points Thus, the remaining outline is obtained.

[0076] Step 2.4: Cluster the contour points in the remaining contours whose index values ​​differ by 1 into one class, and each class corresponds to a corner on the contour. In this way, all adjacent contour points can be clustered into corners in turn.

[0077] Step 3, for each corner, the radius of curvature is greater than After deleting the contour points, the abnormal curvature angle division method is used to perform angle division on the remaining contour points in each angle, resulting in a set of normal angles:

[0078] Step 3.1: Calculate the radius of curvature of each contour point at any corner, and set the radius of curvature greater than 1. Delete the outline points to obtain the remaining angles;

[0079] Step 3.2: Determine whether the contour point corresponding to the maximum radius of curvature of each point in the remaining angle is located on the boundary of its own angle; if yes, proceed to step 3.3; otherwise, proceed to step 3.5.

[0080] Step 3.3: Determine whether the quotient of the maximum radius of curvature divided by the minimum radius of curvature at each point in the remaining angle is greater than... , if yes, delete the profile point of the maximum curvature radius in the corresponding angle, and return to step 3.3 for execution, otherwise, take the corresponding angle as a normal angle and add it to the normal angle set.

[0081] Step 3.4, judge whether the number of profile points of each angle in the normal angle set is less than 3, if yes, delete the corresponding angle, otherwise, keep it unchanged, thereby obtaining the final normal angle set, and executing step 4;

[0082] Step 3.5, take the profile point index corresponding to the maximum curvature radius , and divide the profile points of the corresponding angle into left and right segments with the index as the boundary, take each segment as a new angle, and then take each new angle as the remaining angle and execute in sequence according to step 3.2;

[0083] Step 4, find the angle circle tangent to the normal angle and meeting the 2D Wadell sphericity by using the re-fitting method, the angle circle meeting the 2D Wadell sphericity requires that the angle circle falls within the profile of the zircon particle and the radius of the angle circle is less than the maximum inscribed circle radius of the profile , thereby calculating the 2D Wadell sphericity.

[0084] Step 4.1, calculate the first derivative of the curvature radius of each profile point on any normal angle, and sort each profile point on the normal angle in ascending order according to the absolute value of the first derivative, obtaining the sorted angle point sequence ;

[0085] Step 4.2, calculate the curvature circle center of the first point of the angle point sequence by using formula (4) and take it as the center of the angle circle:

[0086] (4)

[0087] In formula (4), and respectively represent the first derivatives of and , and represents the curvature at point .

[0088] Step 4.3, calculate the curvature radius of the first point of the angle point sequence and take it as the radius of the angle circle;

[0089] Step 4.4, according to the center and radius of the angle circle, judge whether the angle circle is within the profile of the zircon particle, if yes, add the corresponding angle circle to the angle circle set​ In the middle; otherwise, the first point. from After deletion, return to step 4.2 and execute sequentially to obtain the final set of corner circles. In practical applications, the angle circle set The visualization results are as follows Figure 2 As shown.

[0090] Step 4.5: Calculate the final roundness of the zircon grains in the zircon image using equation (5). :

[0091] (5)

[0092] In equation (5), Represents the final angle circle set The radius of the s-th corner circle in the set, where N represents the final set of corner circles. The total number of mid-angle circles.

[0093] This invention is highly efficient and accurate, capable of precisely measuring the two-dimensional Wadell roundness of zircon, saving computational costs while ensuring the reliability of measurement results, and contributing to geotechnical engineering research.

[0094] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in performing the above-described calculation of the 2D Wadell roundness of a zircon image. The processor is configured to execute the program stored in the memory.

[0095] In this embodiment, a computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps described above for calculating the 2D Wadell roundness of a zircon image.

Claims

1. A 2D Wadell roundness calculation method for zircon images based on curvature, characterized in that, Includes the following steps: Step 1: Acquire zircon images and detect the contours of the zircon grains. Then, use a cyclic pseudo-roundness determination method to interpolate and smooth the contours of the zircon grains sequentially to obtain the preprocessed contours of the zircon grains. Step 1.1: Obtain a zircon image and extract the outline of its zircon grains to obtain the zircon grain outlines. And calculate the maximum inscribed circle radius of the profile. ;in, Indicates the first M represents the total number of contour points of the zircon grain. make The coordinates are as ; Step 1.2: Use equation (1) to obtain the first part of the zircon grain profile. Contour points curvature Thus obtain The reciprocal of the first digit is used as the second digit. Contour points radius of curvature ; (1) Step 1.3: Calculate the pseudo-roundness of the zircon grain profile using equation (2). : (2) Step 1.4: Calculate the Euclidean distance between any two adjacent points in the profile of the zircon grain, thus obtaining the set of Euclidean distances. ,in, Indicates the first Contour points and the Contour points The Euclidean distance; Step 1.5, Calculation variance ,when Greater than 3× Then in and Between Sublinear interpolation is used to obtain the interpolated contour. Step 1.6: Perform the interpolation on the contour. After smoothing with a second-Gaussian filter, the pseudo-circularity of the smoothed contour is then calculated. ; Step 1.7, if the difference in pseudo-roundness Greater than a given threshold If the result is positive, the smoothed contour will be carried into step 1.2 and executed sequentially; otherwise, the smoothed contour will be used as the pre-processed contour of the zircon particles, and the process will proceed to step 2. Step 2: Use the vector cross product method to determine the concavity / convexity of the preprocessed contour, and retain the convex arc segments as the contour angles: Step 2.1: Traverse the contour points in the preprocessed contour and find the set of contour points whose ordinates have the maximum values. and from the contour point set Find the contour point with the largest x-coordinate Calculate contour points Adjacent to the previous point The vector formed and outline points With the next adjacent point The vector formed Cross product between ; Step 2.2: For the preprocessed contour... Contour points ,calculate and the previous adjacent point The vector formed as well as Contour of the next adjacent point The vector formed Cross product between ; Step 2.3, if If less than 0, it means the first... Contour points If it belongs to a convex arc segment, otherwise, delete the first segment from the preprocessed contour. Contour points Thus, the remaining outline is obtained; Step 2.4: Cluster the contour points in the remaining contours whose index values ​​differ by 1 into one class, and each class corresponds to a corner on the contour; Step 3, for each corner, the radius of curvature is greater than After deleting the contour points, the abnormal curvature angle division method is used to perform angle division on the remaining contour points in each angle, resulting in a set of normal angles, specifically including: Step 3.1: Calculate the radius of curvature of each contour point at any corner, and set the radius of curvature greater than 1. Delete the outline points to obtain the remaining angles; Step 3.2: Determine whether the contour point corresponding to the maximum radius of curvature of each point in the remaining angle is located on the boundary of its own angle; if yes, proceed to step 3.3; otherwise, proceed to step 3.

5. Step 3.3: Determine whether the quotient of the maximum radius of curvature divided by the minimum radius of curvature at each point in the remaining angle is greater than... If yes, delete the contour point with the maximum radius of curvature in the corresponding angle and return to step 3.3; otherwise, treat the corresponding angle as a normal angle and add it to the normal angle set. Step 3.4: Determine whether the number of contour points of each angle in the normal angle set is less than 3. If so, delete the corresponding angle; otherwise, leave it unchanged to obtain the final normal angle set and proceed to step 4. Step 3.5: Obtain the contour point index corresponding to the maximum radius of curvature. and index Using the boundary as the boundary, the contour points of the corresponding angle are divided into left and right segments. Each segment is regarded as a new angle, and each new angle is used as the remaining angle. Then, the process is carried out in the order of step 3.

2. Step 4: Use the refitting method to find the corner circle that is inscribed in the normal angle and conforms to 2D Wadell roundness, and then calculate the 2D Wadell roundness. : Step 4.1: Calculate the first derivative of the radius of curvature of each contour point on any normal angle, and sort the contour points on the normal angle in ascending order according to the absolute value of the first derivative, to obtain the sorted corner point sequence. ; Step 4.2: Calculate the corner point sequence The first point Center of the curvature circle And use it as the center of the corner circle to calculate the corner point sequence. The first point The radius of curvature is used as the radius of the corner circle; Step 4.3: Based on the center and radius of the corner circle, determine whether the corner circle is within the outline of the zircon grain. If so, then add the corresponding angle circle to the angle circle set. In the middle; otherwise, the first point. from After deletion, return to step 4.2 and execute sequentially to obtain the final set of corner circles. ; Step 4.4: Calculate the final roundness of the zircon grains in the zircon image using equation (3). : (3) In equation (3), Represents the final angle circle set The radius of the s-th corner circle in the set, where N represents the final set of corner circles. The total number of mid-angle circles.

2. The method for calculating the 2D Wadell roundness of zircon images based on curvature according to claim 1, characterized in that, The number of interpolation points in step 1.5 Determine using equation (4): (4) In equation (4), Indicates taking the mode. It is the symbol for rounding up; This represents the threshold value, and its range is [value range missing]. .

3. The 2D Wadell roundness calculation method for zircon images based on curvature according to claim 1, characterized in that, The center of the curvature circle in step 4.2 Calculated using equation (5): (5) In equation (5), and They represent and The first derivative, Point The curvature at that point.

4. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store programs that support the processor in executing the 2D Wadell roundness method for calculating digital images of zircon grains as described in any of claims 1-3, the processor being configured to execute the programs stored in the memory.

5. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is run by the processor, it performs the steps of the 2D Wadell roundness method for calculating the digital image of zircon grains as described in any of claims 1-3.

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