2D Wadell roundness calculation method of zircon image based on curvature

Abstract

The invention discloses a 2D Wadell roundness calculation method of a zircon image based on curvature, which comprises the following steps of: 1, acquiring a zircon image, detecting the contour of the zircon, calculating the maximum inscribed circle radius of the contour, and sequentially interpolating and smoothing the zircon contour by using a cyclic pseudo roundness judgment method, 2, judging the concavity and convexity of points on the contour by using a vector cross product method, the method comprises the following steps of: (1) selecting an inscribed circle as a contour, reserving a convex arc section as an angle of the contour, (2) deleting points of which the curvature radius is greater than the radius of the maximum inscribed circle in the angle, and then carrying out further angle division operation on residual points of the angle by utilizing an SC method, and (4) searching an angle circle which is internally tangent to the angle and conforms to the definition of the 2D Wadell roundness by utilizing a refitting method, and finally calculating the 2D Wadell roundness. According to the method, the 2D Wadell roundness of the contour can be rapidly and accurately detected, the labor cost of manually drawing an angle circle in the prior art is reduced, the detection efficiency can be improved, and related resource environment work can be developed.

Description

Technical Field

[0001] The invention belongs to the field of material science and mineralogy, and in particular relates to a 2D Wadell roundness calculation method of a zircon image based on curvature. Background Art

[0002] The shape of granular materials has an impact on many engineering and technical fields. Calculating the shape parameters of mineral particles helps to understand important information about the sedimentary environment, geological history and formation process of the particles. Among them, 2D Wadell roundness is a widely used indicator to describe the relative sharpness of particle corners. In the traditional calculation of zircon 2D Wadell roundness, when computer hardware performance is not yet developed, researchers need to manually compare the radius of curvature of each corner of the zircon particle with the radius of curvature of the circular aperture ruler. This measurement method is highly dependent on manpower and has low efficiency. Even completing the roundness calibration calculation of a single zircon particle requires a high time cost.

[0003] At present, the two-dimensional contour information of particles can be obtained through digital image processing and three-dimensional scanning methods, 2D Wadell roundness calculation can be performed, and the radius of curvature can be estimated by fitting the corner circle at the fillet. The biggest advantage of digital image processing is low cost, convenient acquisition, and small amount of data. The obtained particle contour is representative, and extremely fine particles (such as rock slices) can be imaged through a microscope.

[0004] However, due to the nature of digital images being a matrix of pixels, particle outlines derived from images inevitably have jagged edges - a small range of random errors that usually have no clear directionality and fluctuate around the true value. However, 2D Wadell circularity is highly sensitive to jagged edges around particle outlines. Since the calculation of the radius of curvature depends on the overall smoothness of the identified scale, the presence of jagged edges can lead to significant fluctuations in curvature. If the jagged edges are not removed, there is a risk of identifying edges as particle corners.

[0005] Therefore, based on the above reasons, Reference 1: Vangla, P., Roy, N. & Gali, ML Image based shape 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 the particle contour, and the smoothing effect is significant. 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 contour is transformed into the frequency domain by Fourier transform to obtain a smooth particle contour. Reference 3: Chen, J., Zhang, Z., Lin, D., Li,L., & Xu, W. (2024). An improved corner dealiasing and recognition algorithmfor 2D Wadell roundness computation. Scientific Reports, 14(1), 9439. The contour is denoised using the cyclic median filtering method, and a corresponding line graph of the number of cycles and the error range is provided. However, these methods are difficult to balance the smoothness and non-deformation of the particle contour during the denoising process, and the method of converting the particle contour into the frequency domain has problems such as low computational efficiency and difficulty in fitting sharp corners when fitting details, resulting in generally blunt results. Summary of the invention

[0006] In order to solve the shortcomings of the above-mentioned prior art, the present invention proposes a 2D Wadell roundness calculation method for zircon images based on curvature, so as to quickly and accurately detect the 2D Wadell roundness of the contour, reduce the labor cost of manually drawing corner circles, and improve the detection efficiency. It can be applied to the quantitative research of particle shape in multiple related fields.

[0007] The present invention adopts the following technical solutions to solve the technical problems:

[0008] The 2D Wadell roundness calculation method of a zircon image based on curvature of the present invention is characterized in that it comprises the following steps:

[0009] Step 1, obtaining a zircon image and detecting the contours of its zircon particles, and using a cyclic pseudo-roundness determination method to sequentially interpolate and smooth the contours of the zircon particles to obtain a preprocessed contour of the zircon particles;

[0010] Step 2, using the vector cross product method to determine the concavity and convexity of the preprocessed contour, and retaining the convex arc segment as the corner of the contour;

[0011] Step 3: Set the radius of curvature of each corner to be greater than After deleting the contour points, the abnormal curvature angle division method is used to divide the remaining contour points in each corner to obtain a normal angle set;

[0012] Step 4: Use the refitting method to find the corner circle that is inscribed in the normal angle and meets the 2D Wadell roundness, so as to calculate the 2D Wadell roundness. .

[0013] The 2D Wadell roundness calculation method of a zircon image based on curvature described in the present invention is also characterized in that the step 1 comprises the following steps:

[0014] Step 1.1, obtain a zircon image and extract the outline of its zircon particles, and obtain the outline of the zircon particles , and calculate the maximum inscribed circle radius of the contour ;in, Indicates contour points, M represents the total number of contour points of zircon particles;

[0015] make The coordinates of ;

[0016] Step 1.2: Use formula (1) to obtain the first Contour points Curvature , thus taking The reciprocal of Contour points The radius of curvature ;

[0017] (1)

[0018] Step 1.3: Calculate the pseudo-roundness of the zircon particle outline using formula (2): :

[0019] (2)

[0020] Step 1.4: Calculate the Euclidean distance between any adjacent contour points in the contour of the zircon particle to obtain the Euclidean distance set ,in, Indicates Contour points and Contour points The Euclidean distance of

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

[0022] (3)

[0023] In formula (3), It means taking the majority, is the sign for rounding up; Represents the threshold value, and its value range is ;

[0024] Step 1.6: Calculation Variance ,when Greater than 3× , then in and Between Sublinear interpolation is performed to obtain the interpolated contour;

[0025] Step 1.7: Perform the interpolated contour After sub-Gaussian filtering, the pseudo-roundness of the smoothed contour is calculated. ;

[0026] Step 1.8: If the difference in pseudo-circularity Greater than a given threshold , then bring the smoothed contour into step 1.2 and execute sequentially; otherwise, take the smoothed contour as the pre-processed contour of the zircon particle and go to step 2.

[0027] Furthermore, the step 2 comprises the following steps:

[0028] Step 2.1: Traverse the contour points in the preprocessed contour and find the set of contour points with the maximum ordinate. , and from the contour point set Find the contour point with the largest horizontal coordinate , calculate the contour points The previous adjacent point The vector composed And contour points The next adjacent point The vector composed The cross product between ;

[0029] Step 2.2: Contour points ,calculate and the previous adjacent point The vector composed as well as The next adjacent point The vector composed The cross product between ;

[0030] Step 2.3: If Less than 0, it means Contour points Belongs to a convex arc segment, otherwise, delete the first Contour points ; Thus, the remaining contour is obtained;

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

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

[0033] Step 3.1, calculate the radius of curvature of each contour point on any corner, and add the radius of curvature greater than Delete the contour points and get the remaining corners;

[0034] Step 3.2, determine whether the contour point corresponding to the maximum curvature radius of each point in the remaining angle is located at the boundary of the own angle; if so, execute step 3.3, otherwise, execute step 3.5;

[0035] Step 3.3: Determine whether the quotient of the maximum value of the curvature radius of each point in the remaining angle divided by the minimum value is greater than If yes, delete the contour point with the maximum curvature radius 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 corner in the normal corner set is less than 3. If so, delete the corresponding corner, otherwise keep it unchanged, so as to obtain the final normal corner set and execute step 4;

[0037] Step 3.5: Take the index of the contour point corresponding to the maximum curvature radius , and indexed by As the boundary, the contour points of the corresponding corner are divided into left and right segments, and each segment is regarded as a new corner, so that each new corner is regarded as the remaining corner, and the steps 3.2 are executed sequentially.

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

[0039] Step 4.1. Calculate the first-order derivative of the radius of curvature of each contour point on any normal corner, and sort each contour point on the normal corner in ascending order according to the absolute value of the first-order derivative to obtain the sorted corner point sequence. ;

[0040] Step 4.2: Calculate the corner point sequence using formula (4) The first point The center of the circle of curvature and as the center of the corner circle:

[0041] (4)

[0042] In formula (4), and Respectively and The first derivative of Indicate point The curvature at

[0043] Step 4.3: Calculate the corner point sequence The first point The curvature radius is used as the radius of the corner circle;

[0044] Step 4.4: Determine whether the corner circle is within the contour of the zircon particle based on the center and radius of the corner circle. If yes, add the corresponding corner circle to the corner circle set Otherwise, the first point from After deleting, return to step 4.2 and execute sequentially to obtain the final corner circle set ;

[0045] Step 4.5: Calculate the final roundness of the zircon particles in the zircon image using formula (5) :

[0046] (5)

[0047] In formula (5), Represents the final set of corner circles The radius of the sth corner circle in, N represents the final corner circle set The total number of mid-corner circles.

[0048] The electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports 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 present invention provides a computer-readable storage medium, and the computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, executes the steps of the 2D Wadell roundness method for calculating a digital image of zircon particles.

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

[0051] 1. The present invention proposes a cyclic pseudo-roundness determination method to perform interpolation-smoothing processing on the zircon contour. The contour that maintains the original shape of the zircon particles can be obtained without manually determining the number of cyclic smoothing times, which can improve the efficiency of zircon 2D Wadell roundness calculation without losing accuracy.

[0052] 2. The present invention proposes to use the vector cross product method to determine the convexity of points on the contour, which can accurately identify the convex arc segments in the smoothed contour as contour angles while simplifying calculations, thereby providing a scientific and reasonable new solution for angle identification.

[0053] 3. The abnormal curvature angle division method proposed in the present invention can effectively identify two corners that are difficult to identify due to their close distance, thereby improving the 2D Wadell roundness accuracy of zircon particles, thereby helping to reduce subtle errors in the calibration process and achieving a balance between maintaining accuracy and reducing sawtooth noise.

[0054] 4. The refitting method proposed in the present invention can accurately fit the corner circle that conforms to the 2D Wadell definition when the corner tip is blurred due to a blunt corner. Compared with the least squares fitting method used in previous methods to calculate the corner circle, it can better find the corner circle that is truly inscribed in the corner, alleviating the problem of the roundness calculation results being too large due to the use of the least squares method. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flow chart of the method of the present invention;

[0056] Figure 2 This is a visualization result diagram of the practical application of the method of the present invention. DETAILED DESCRIPTION

[0057] In this embodiment, when carrying out geological engineering, a 2D Wadell roundness calculation method for zircon images based on curvature proposed in the present invention can be used to quickly and conveniently calibrate the roundness of zircon, thereby determining the transportation time, transportation distance, formation history, and type of mechanical action during the formation process of the zircon; in hydraulic fracturing research, the present invention can be used to screen large quantities of special hydraulic fracturing sand without sharp corners; in macro and micro geotechnical engineering, the present invention can be used to accurately and quantitatively evaluate the microscopic morphological characteristics of natural sand, and then determine its mechanical properties and applicable scenarios. In actual operation, compared with previous methods, the cyclic pseudo-roundness determination method used in the present invention can maintain the shape of zircon without manually adjusting the number of smoothing times, and does not sacrifice calculation accuracy. The present invention uses the vector cross product method and the abnormal curvature angle division method to efficiently and accurately identify all corners in the contour, and applies the refitting method to avoid the problem of roundness dullness caused by least squares fitting to a certain extent. Specifically, if Figure 1 As shown, the following steps are included:

[0058] Step 1: Obtain a zircon image and detect the contours of its zircon particles, and use a cyclic pseudo-roundness determination method to interpolate and smooth the contours of the zircon particles in turn:

[0059] Step 1.1, obtain a zircon image, and use the image segmentation model FastSAM to identify the foreground object zircon in the image, apply a binary mask to it, and then extract the outline of the zircon particles through the image topology analysis algorithm proposed by Satoshi Suzuki in 1985 ,in, Indicates contour points, M represents the total number of contour points of the zircon particle, and the shortest distance graph from each point in the zircon particle to the contour is calculated. The center of the largest inscribed circle is the point farthest from the internal contour of the particle; the maximum distance in the distance graph is the radius of the largest inscribed circle of the contour ;

[0060] make The coordinates of .

[0061] Step 1.2: Use formula (1) to obtain the first Contour points Curvature , thus taking The reciprocal of Contour points The radius of curvature ;

[0062] (1)

[0063] Step 1.3: Calculate the pseudo-roundness of the zircon particle outline using formula (2): :

[0064] (2)

[0065] Step 1.4: Calculate the Euclidean distance between any adjacent contour points in the contour of the zircon particle to obtain the Euclidean distance set ,in, Indicates Contour points and Contour points The Euclidean distance of .

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

[0067] (3)

[0068] In formula (3), It means taking the majority, is the sign for rounding up; Represents the threshold value, and its value range is ;

[0069] Step 1.6: Calculation Variance ,according to Principle, when Greater than 3× , indicating the distance Abnormal, then and Between Sublinear interpolation is performed to obtain the interpolated contour.

[0070] Step 1.7: Perform the interpolated contour After sub-Gaussian filtering, the pseudo-roundness of the smoothed contour is calculated. ;

[0071] Step 1.8: If the difference in pseudo-circularity Greater than a given threshold , indicating that there is still aliased noise on the contour that has not been eliminated, then the smoothed contour is brought into step 1.2 and executed sequentially; otherwise, the smoothed contour is used as the preprocessed contour of the zircon particle and go to step 2.

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

[0073] Step 2.1: Traverse the contour points in the preprocessed contour and find the set of contour points with the maximum ordinate. , and from the contour point set Find the contour point with the largest horizontal coordinate , calculate the contour points The previous adjacent point The vector composed And contour points The next adjacent point The vector composed The cross product between ;

[0074] Step 2.2: Contour points ,calculate and the previous adjacent point The vector composed as well as The next adjacent point The vector composed The cross product between ;

[0075] Step 2.3: If Less than 0, it means Contour points Belongs to a convex arc segment, otherwise, delete the first Contour points ; thus obtaining the remaining contours.

[0076] Step 2.4: Cluster the remaining contour points 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: Set the radius of curvature of each corner to be greater than After deleting the contour points, the abnormal curvature angle division method is used to divide the remaining contour points in each corner to obtain the normal angle set:

[0078] Step 3.1, calculate the radius of curvature of each contour point on any corner, and add the radius of curvature greater than Delete the contour points and get the remaining corners;

[0079] Step 3.2, determine whether the contour point corresponding to the maximum curvature radius of each point in the remaining angle is located at the boundary of the own angle; if so, execute step 3.3, otherwise, execute step 3.5;

[0080] Step 3.3: Determine whether the quotient of the maximum value of the curvature radius of each point in the remaining angle divided by the minimum value is greater than If so, delete the contour point with the maximum curvature radius 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.

[0081] Step 3.4: Determine whether the number of contour points of each corner in the normal corner set is less than 3. If so, delete the corresponding corner, otherwise keep it unchanged, so as to obtain the final normal corner set and execute step 4;

[0082] Step 3.5: Take the index of the contour point corresponding to the maximum curvature radius , and indexed by As the boundary, divide the contour points of the corresponding corner into left and right segments, regard each segment as a new corner, and then regard each new corner as the remaining corner, and execute in sequence according to step 3.2;

[0083] Step 4: Use the refitting method to find a corner circle that is inscribed in the normal angle and conforms to the 2D Wadell roundness. The corner circle that conforms to the 2D Wadell roundness requires that the corner circle falls within the contour of the zircon grain and the radius of the corner circle is smaller than the maximum inscribed circle radius of the contour. , and thus calculate the 2D Wadell circularity.

[0084] Step 4.1. Calculate the first-order derivative of the radius of curvature of each contour point on any normal corner, and sort each contour point on the normal corner in ascending order according to the absolute value of the first-order derivative to obtain the sorted corner point sequence. ;

[0085] Step 4.2: Calculate the corner point sequence using formula (4) The first point The center of the circle of curvature and as the center of the corner circle:

[0086] (4)

[0087] In formula (4), and Respectively and The first derivative of Indicate point The curvature of the .

[0088] Step 4.3: Calculate the corner point sequence The first point The curvature radius is used as the radius of the corner circle;

[0089] Step 4.4: Determine whether the corner circle is within the contour of the zircon particle based on the center and radius of the corner circle. If yes, add the corresponding corner circle to the corner circle set Otherwise, the first point from After deleting, return to step 4.2 and execute sequentially to obtain the final corner circle set ; In practical applications, the angle circle set The visualization results are as follows Figure 2 shown.

[0090] Step 4.5: Calculate the final roundness of the zircon particles in the zircon image using formula (5) :

[0091] (5)

[0092] In formula (5), Represents the final set of corner circles The radius of the sth corner circle in, N represents the final corner circle set The total number of mid-corner circles.

[0093] The present invention is efficient and accurate, can accurately measure the two-dimensional Wadell roundness of zircon, saves calculation costs and ensures the reliability of measurement results, and is helpful for geotechnical engineering research.

[0094] In this embodiment, an electronic device includes a memory and a processor. The memory is used to store a program that supports the processor to execute the above-mentioned calculation of 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, and when the computer program is executed by a processor, the step of calculating the 2D Wadell roundness of the zircon image is performed.

Claims

1. A 2D Wadell roundness calculation method for zircon images based on curvature, characterized in that: The steps include: Step 1, obtaining a zircon image and detecting the contours of its zircon particles, and using a cyclic pseudo-roundness determination method to sequentially interpolate and smooth the contours of the zircon particles to obtain a preprocessed contour of the zircon particles; Step 2, using the vector cross product method to determine the concavity and convexity of the preprocessed contour, and retaining the convex arc segment as the corner of the contour; Step 3: Set the radius of curvature of each corner to be greater than After deleting the contour points, the abnormal curvature angle division method is used to divide the remaining contour points in each corner to obtain a normal angle set; Step 4: Use the refitting method to find the corner circle that is inscribed in the normal angle and meets the 2D Wadell roundness, so as to calculate the 2D Wadell roundness. .

2. The 2D Wadell roundness calculation method of a zircon image based on curvature according to claim 1, characterized in that: The step 1 comprises the following steps: Step 1.1, obtain a zircon image and extract the outline of its zircon particles, and obtain the outline of the zircon particles , and calculate the maximum inscribed circle radius of the contour ;in, Indicates contour points, M represents the total number of contour points of zircon particles; make The coordinates of ; Step 1.2: Use formula (1) to obtain the first Contour points Curvature , thus taking The reciprocal of Contour points The radius of curvature ; (1) Step 1.3: Calculate the pseudo-roundness of the zircon particle outline using formula (2): : (2) Step 1.4: Calculate the Euclidean distance between any adjacent contour points in the contour of the zircon particle to obtain the Euclidean distance set ,in, Indicates Contour points and Contour points The Euclidean distance of Step 1.5: Calculate the number of interpolation points using formula (3) : (3) In formula (3), It means taking the majority, is the sign for rounding up; Represents the threshold value, and its value range is ; Step 1.6: Calculation Variance ,when Greater than 3× , then in and Between Sublinear interpolation is performed to obtain the interpolated contour; Step 1.7: Perform the interpolated contour After sub-Gaussian filtering, the pseudo-roundness of the smoothed contour is calculated. ; Step 1.8: If the difference in pseudo-circularity Greater than a given threshold , then bring the smoothed contour into step 1.2 and execute sequentially; otherwise, take the smoothed contour as the pre-processed contour of the zircon particle and go to step 2.

3. The 2D Wadell roundness calculation method of a zircon image based on curvature according to claim 2, characterized in that: The step 2 comprises the following steps: Step 2.1: Traverse the contour points in the preprocessed contour and find the set of contour points with the maximum ordinate. , and from the contour point set Find the contour point with the largest horizontal coordinate , calculate the contour points The previous adjacent point The vector composed And contour points The next adjacent point The vector composed The cross product between ; Step 2.2: Contour points ,calculate and the previous adjacent point The vector composed as well as The next adjacent point The vector composed The cross product between ; Step 2.3: If Less than 0, it means Contour points Belongs to a convex arc segment, otherwise, delete the first Contour points ; Thus, the remaining contour is obtained; Step 2.4: Group the remaining contour points whose index values ​​differ by 1 into one class, and each class corresponds to a corner on the contour.

4. The 2D Wadell roundness calculation method of a zircon image based on curvature according to claim 3, characterized in that: The step 3 comprises the following steps: Step 3.1, calculate the radius of curvature of each contour point on any corner, and add the radius of curvature greater than Delete the contour points and get the remaining corners; Step 3.2, determine whether the contour point corresponding to the maximum curvature radius of each point in the remaining angle is located at the boundary of the own angle; if so, execute step 3.3, otherwise, execute step 3.5; Step 3.3: Determine whether the quotient of the maximum value of the curvature radius of each point in the remaining angle divided by the minimum value is greater than If yes, delete the contour point with the maximum curvature radius 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 corner in the normal corner set is less than 3. If so, delete the corresponding corner, otherwise keep it unchanged, so as to obtain the final normal corner set and execute step 4; Step 3.5: Take the index of the contour point corresponding to the maximum curvature radius , and indexed by As the boundary, the contour points of the corresponding corner are divided into left and right segments, and each segment is regarded as a new corner, so that each new corner is regarded as the remaining corner, and the steps 3.2 are executed sequentially.

5. The 2D Wadell roundness calculation method of a zircon image based on curvature according to claim 4, characterized in that: The step 4 comprises the following steps: Step 4.

1. Calculate the first-order derivative of the radius of curvature of each contour point on any normal corner, and sort each contour point on the normal corner in ascending order according to the absolute value of the first-order derivative to obtain the sorted corner point sequence. ; Step 4.2: Calculate the corner point sequence using formula (4) The first point The center of the circle of curvature and as the center of the corner circle: (4) In formula (4), and Respectively and The first derivative of Indicate point The curvature at Step 4.3: Calculate the corner point sequence The first point The curvature radius is used as the radius of the corner circle; Step 4.4: Determine whether the corner circle is within the contour of the zircon particle based on the center and radius of the corner circle. If yes, add the corresponding corner circle to the corner circle set Otherwise, the first point from After deleting, return to step 4.2 and execute sequentially to obtain the final corner circle set ; Step 4.5: Calculate the final roundness of the zircon particles in the zircon image using formula (5) : (5) In formula (5), Represents the final set of corner circles The radius of the sth corner circle in, N represents the final corner circle set The total number of mid-corner circles.

6. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the 2D Wadell roundness method for calculating the digital image of zircon particles as described in any one of claims 1 to 5, and the processor is configured to execute the program stored in the memory.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for calculating the 2D Wadell roundness of a digital image of zircon particles as claimed in any one of claims 1 to 5 are performed.

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