CN112819810B - Sand particle roundness calculation method - Google Patents
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Abstract
The invention provides a sand particle roundness calculation method, which comprises the following steps: step 100, microscopic photographing is carried out on sand particle clusters to be detected in a roundness grinding mode, and microscopic images of sand particles are obtained; step 200, converting the obtained microscopic image into a gray level image, distinguishing different sand particles from the gray level image by using an image segmentation technology, and then converting the gray level image into a binary image; step 300, acquiring sand particle outline pixels in the obtained binary image, extracting pixel coordinates of all sand particle outlines, and removing sand particles exceeding the image boundary; and 400, performing discrete geometric analysis on the obtained sand particle contour pixel coordinates, and calculating to obtain the roundness grinding parameters of the sand particles. The sand particle roundness calculation method provided by the invention solves the problem that the conventional evaluation result is influenced by subjective selection of a tester, can rapidly determine the roundness of sand particles, has objective, accurate and reliable calculation result, and can help a numerical simulation researcher to generate a more real particle flow model.
Description
Technical Field
The invention relates to the field of quantification of sand particle shapes, in particular to a sand particle roundness calculation method.
Background
As discrete element sand numerical analysis matures, it becomes imperative to utilize the true particle geometry in the model. But how to effectively determine the particle morphology of real soil is a challenge. Roundness as a parameter describing the degree of blunting of the corner edges of sand particles is a very important morphological parameter.
However, the conventional method of visual inspection cannot obtain accurate results of all parameters, and the existing roundness calculation method is poor in stability and rapidness, so that a method capable of rapidly and accurately calculating the roundness of sand particles is needed to be invented.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a sand particle roundness calculation method, which utilizes microscopic images of sand particles, is based on an image processing technology, can rapidly determine the roundness of the sand particles, has objective, accurate and reliable calculation results, and can help numerical simulation researchers to generate a more real particle flow model.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
a sand particle roundness calculation method comprises the following steps:
step 100, microscopic photographing is carried out on sand particle clusters to be detected in a roundness grinding mode, and microscopic images of sand particles are obtained;
step 200, converting the obtained microscopic image into a gray level image, distinguishing different sand particles from the gray level image by using an image segmentation technology, and then converting the gray level image into a binary image;
step 300, acquiring sand particle outline pixels in the obtained binary image, extracting pixel coordinates of all sand particle outlines, and removing sand particles exceeding the image boundary;
and 400, performing discrete geometric analysis on the obtained sand particle contour pixel coordinates, and calculating to obtain the roundness grinding parameters of the sand particles.
Optionally, in step 200, when different sand particles are distinguished, the sand particles are colored first and then image segmentation is performed.
Optionally, in step 300, the acquiring the sand particle contour pixel in the obtained binary image specifically includes: the background of the binary image is black, particles are white, white connected domains in the image are obtained one by one, each white pixel in each connected domain is traversed, and when black pixels exist in upper, lower, left and right adjacent pixels of the pixel or the pixels are image boundaries, the pixels are judged to be particle contour pixels.
Optionally, in step 400, the calculation of the roundness is specifically:
1) Calculating the maximum inscribed circle radius R of the sand particles by using the outline pixel coordinates of the sand particles;
2) Identifying each edge angle of the sand particles, recording the number of the edge angles as N, and fitting each edge angle circle in sequence by using a least square method to obtain the curvature radius r of each edge angle i ；
3) Calculating the roundness n of the sand particles according to formula (1):
wherein r is i The radius of curvature of the particle corners is represented, R represents the maximum inscribed circle radius of the particles, and N represents the number of particle corners.
Optionally, the identifying of the sand particle edges includes identifying edge key points, the identifying of the edge key points includes smoothing the particle outline, and the identifying specifically includes:
the first step, sequentially connecting the pixel points of the outline of the sand particles into line segments to form a closed graph, wherein the closed graph is the original outline of the sand particles;
secondly, taking the middle points of all line segments in the original profile of the sand particles, and sequentially connecting the middle points of all line segments into a new profile of the sand particles, wherein the new profile of the sand particles is circulated for 1 time;
and thirdly, iterating according to the method of the second step on the basis of the sand particle profile obtained by calculation of the second step, so as to obtain the sand particle profile of the cycle for n times, and exiting the cycle until the sand particle profile is smooth.
Optionally, the identifying of the corner key points further includes marking of the corner key points of the particles, specifically:
taking 3 adjacent contour coordinate points from the smoothed particle contour as a circle, and marking the middle points of the 3 points as key points of the particle edges and corners if the circle simultaneously meets the following three conditions, namely (a) the circle center is in the particle contour, (b) the radius is smaller than the maximum inscribed circle radius, and (c) the circle does not exceed the particle contour.
Optionally, the identifying of the edges of the sand particles further comprises edge key point grouping, wherein the edge key point grouping refers to dividing the key points into groups according to different edges, the key point grouping comprises preliminary grouping, and the preliminary grouping is set by adopting a statistical methodPut a length d f When the distance d between two adjacent corner key points is smaller than d f When the two corner key points are in the same group, otherwise, the two corner key points are in different groups.
Optionally, d in the preliminary packet f The setting of (2) comprises the following 3 steps:
1) Calculating the distance between two adjacent key edge points to obtain the maximum distance d max And a minimum distance d min ；
2) Calculating a distance normalization value P of two adjacent edge angle key points by using a formula (2):
the interval with dense P value distribution corresponds to the particle corner area, and the interval with sparse P value distribution corresponds to the non-corner area;
3) To further distinguish P values as dense intervals or sparse intervals, a grouping coefficient a is introduced so that P E [0, a ] is the dense interval, P E (a, 1)]When the time is a sparse interval, d is calculated by using the formula (3) f ：
d f ＝a×(d max -d min )+d min (3)
The value a is determined by counting the distribution of normalized values P of two adjacent corner key points of a plurality of particle images, and d obtained by the formulas (2) and (3) is d when P=a f 。
Optionally, performing the calculation of the edge and corner circles on the preliminary grouping result of the particle edge and corner key points, and performing fine grouping on the preliminary grouping result of the particle edge and corner key points by using a dichotomy when one of the following three conditions exists in the edge and corner circles calculated by the preliminary grouping:
case one: the fitted corner circles exceed the grain boundaries;
and a second case: goodness of fit R of the fitted angular circle 2 Too low;
and a third case: the central angle corresponding to the key point of the edge angle is too small.
Optionally, the fine grouping is to divide the grouping into two groups from the maximum interval in the group, and fit the two groups to circles respectively; and if the three conditions still exist, repeating the two halves for the new group until the fitted circle does not exist or the number of the grouped points is less than 3.
Compared with the prior art, the invention has the remarkable characteristics that:
(1) The sand particle roundness calculation method provided by the invention solves the problem that the conventional evaluation result is influenced by subjective selection of a tester.
(2) The roundness calculation method provided by the invention is more objective and rapid:
firstly, in the aspect of sand particle contour smoothing, a method of connecting points of a circulation line segment is adopted, so that the calculation speed is high, and the smoothing effect is good; secondly, marking coordinate points with curvature radius smaller than the maximum inscribed circle radius in the smoothed particle contour coordinates, namely corner key points, wherein the marking of the corner key points can reduce the searching range of the corner circles; then, the corner key points are independently grouped according to the difference of the attribution corners, so that each corner of the particles corresponds to a plurality of corner key points, and the accidental recognition of the corners is reduced while the number of corner circle fitting steps is further reduced; and finally, fitting the key points of the edges and corners of the groups by using a least square method, wherein the condition of gradual curvature change does not exist, and the curvature radius representing the edges and corners does not need to be selected from a plurality of curvature radii.
(3) The method can simultaneously calculate the roundness of a plurality of sand particles by using an image segmentation method.
(4) The roundness grinding parameter provided by the invention is not greatly influenced by the image resolution, only the minimum diameter pixel number of the circumscribed circles of particles is required to be more than 200 pixels, and the calculation result is not influenced by the image resolution.
Drawings
FIG. 1 is a binary image of a certain sand particle cluster;
FIG. 2 is a schematic view of the sand particle profile extraction of FIG. 1;
FIG. 3 is a flowchart of a roundness calculation method according to an embodiment of the present invention;
FIG. 4 is a schematic illustration of a sand particle profile (partial) smoothing process;
FIG. 5 is a comparison of sand grain profile smoothing before and after;
fig. 6 is a schematic diagram of calculation results and calculation values of sand particle roundness and corner circles.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the embodiments and the accompanying drawings. The exemplary embodiments of the present invention and their descriptions herein are for the purpose of explaining the present invention, but are not to be construed as limiting the invention.
The roundness pi is used for describing the sharpness degree of the edge angle of the sand particles, and is calculated by referring to the following formula (1):
the calculation formula of the roundness II:
wherein r is i The radius of curvature of the particle corners is represented, R represents the maximum inscribed circle radius of the particles, and N represents the number of particle corners.
On the basis of the above work, the present invention specifically gives the following examples to explain in detail the sand particle roundness calculation method.
As shown in fig. 1, which is a binary diagram of a certain sand particle cluster, the roundness parameters of the diagram are calculated, and the specific steps are as follows:
step 100, fixing sand particle clusters to be detected in a roundness grinding manner on a glass slide, and carrying out microscopic photographing to obtain microscopic images of sand particles;
step 200, converting the obtained microscopic image into a gray level image, distinguishing different sand particles from the gray level image by using a threshold segmentation method in an image segmentation technology, and then converting the gray level image into a binary image;
step 300, acquiring sand particle contour pixels in the obtained binary image, extracting pixel coordinates of all particle contours, and removing sand particles exceeding the image boundary, as shown in fig. 2;
in the step, the step of acquiring the sand particle contour pixels in the obtained binary image specifically comprises the following steps: the background of the binary image is black, particles are white, white connected domains in the image are obtained one by one, each white pixel in each connected domain is traversed, and when black pixels exist in upper, lower, left and right adjacent pixels of the pixel or the pixels are image boundaries, the pixels are judged to be particle contour pixels.
And 400, performing discrete geometric analysis on the obtained sand particle contour pixel coordinates, and calculating to obtain the roundness of the sand particles.
The calculation flow of the roundness is shown in fig. 3. Calculating the maximum inscribed circle radius R of the particles by using the pixel coordinates of the particle outline, identifying each edge of the particles, recording the number of the edges as N, and fitting each edge circle in sequence by using a least square method to obtain the curvature radius R of each edge i The roundness of the particles can be obtained from the formula (1).
According to the formula (1), the identification range of the particle edge angle is an edge angle with a curvature radius smaller than the radius of the maximum inscribed circle, and the coordinate point of the edge angle is defined as an edge angle key point. And (3) independently grouping the corner key points according to the difference of the attribution corners, so that each corner of the particles corresponds to a plurality of corner key points. Thus, the identification of the particle edges can be divided into two key steps, namely edge key point identification and edge key point grouping.
First, the identification of the particle edge key points comprises two processes of particle contour smoothing and particle edge key point marking:
(1) The particle image is amplified to form a sawtooth edge, and the lower the resolution is, the larger the fluctuation amplitude of the sawtooth edge accounts for the specific gravity of the particle width, and the larger the influence on the accuracy of particle edge angle identification is, so that the contour of the particle needs to be smoothened. The first step, sequentially connecting the pixel points of the outline of the sand particles into line segments to form a closed graph, wherein the closed graph is the original outline of the sand particles; secondly, taking the middle points of all line segments in the original profile of the sand particles, and sequentially connecting the middle points of all line segments into a new profile of the sand particles, wherein the new profile of the sand particles is circulated for 1 time, as shown in fig. 4; third, based on the sand particle outline obtained by the second calculation, proceeding according to the method of the second stepIterating the rows to obtain the contours of the sand particles in the loop for n times until the contours of the sand particles are smooth, and exiting the loop, wherein the contours R in the loop for 139 times are shown in figure 5 2 =0.995, indicating that the profile of the sand particles is sufficiently close to the original profile, and that the profile of the sand particles is sufficiently smooth.
(2) And marking key points of the edges and corners of the particles by using the smoothed particle profile. Taking the pixel coordinates of the adjacent 3 contours of the smoothed particle contour as a circle, and marking the middle point of the 3 points if the circle center of the circle is positioned inside the particle contour and the radius is smaller than the maximum inscribed circle radius and the circle does not exceed the particle contour. If one of the above three conditions is not satisfied, no marking is performed.
Secondly, dividing the key points into groups according to different edges and angles. These key points make up all the corners. Each group of key points is fitted with a circle and is defined as an angular circle. The corner key point grouping can be divided into a preliminary grouping process and a fine grouping process:
(1) And (5) carrying out preliminary grouping on the key points of the edges and corners of the particles by adopting a statistical analysis method. The key points of the particle edges and corners have the characteristics of being relatively gathered at the same edge and corners and being relatively dispersed at different edges and corners. Set a length d f When the distance d between two adjacent corner key points is smaller than d f When the two corner key points are in the same group; otherwise, the two corner key points are in different groups.
For d f The setting of (2) comprises the following 3 steps:
(a) Calculating the distance between two adjacent key edge points to obtain the maximum distance d max And a minimum distance d min ；
(b) Calculating distance normalization values P of two adjacent edge key points by using a formula (2), wherein a region with dense P value distribution corresponds to a particle edge region, and a region with sparse P value distribution corresponds to a non-edge region;
(c) To further distinguish the P value as dense or sparse intervalThe grouping coefficient a is introduced so that P epsilon [0, a ] is a dense interval, P epsilon [ a,1 ]]And is a sparse interval. The value a can be determined by counting the distribution of normalized values P of adjacent two corner key points of several particle images. When p=a, d obtained by the formula (2) is d f ，d f The calculation is shown in formula (3).
d f ＝a×(d max -d min )+d min (3)
(2) And carrying out the calculation of the edge and corner circles on the results of the preliminary grouping of the particle edge and corner key points. When the calculated edge angle circle exists in one of the following three cases, the primary grouping result of the particle edge angle key points is finely grouped by using a dichotomy.
Case 1: the fitted corner circles exceed the grain boundaries;
case 2: goodness of fit R of the fitted angular circle 2 Too low;
case 3: the central angle corresponding to the key point of the edge angle is too small.
The method of fine grouping is to divide the grouping into two groups from the maximum spacing within the group, and fit the two groups to circles, respectively. If the three conditions still exist, repeating the two halves for the new group until the fitted circle does not exist or the number of the groups is less than 3. As shown in FIG. 6, the calculation results of the corner circles of the particles are shown as well attached to the corresponding corner angles, no macroscopic deviation appears, the calculation results are close to the reference value in the Stratigraphy and sedimentation book published by Krumbein et al (1963), and the accuracy and reliability of the method for calculating the roundness are verified.
By now it will be appreciated by those skilled in the art that while exemplary embodiments of the invention have been shown and described in detail herein, many other variations or modifications which are in accordance with the principles of the invention may be directly ascertained or inferred from the present disclosure without departing from the spirit and scope of the invention. Accordingly, the scope of the present invention should be understood and deemed to cover all such other variations or modifications.
Claims (6)
1. The sand particle roundness calculation method is characterized by comprising the following steps of:
step 100, microscopic photographing is carried out on sand particle clusters to be detected in a roundness grinding mode, and microscopic images of sand particles are obtained;
step 200, converting the obtained microscopic image into a gray level image, distinguishing different sand particles from the gray level image by using an image segmentation technology, and then converting the gray level image into a binary image;
step 300, acquiring sand particle outline pixels in the obtained binary image, extracting pixel coordinates of all sand particle outlines, and removing sand particles exceeding the image boundary;
step 400, performing discrete geometric analysis on the obtained sand particle contour pixel coordinates, and calculating to obtain the roundness grinding parameters of the sand particles; the calculation of the roundness is specifically:
1) Calculating the maximum inscribed circle radius of the sand particles by using the pixel coordinates of the outline of the sand particlesR；
2) Identifying each edge angle of the sand particles, and recording the number of the edge angles as followsNFitting each angular circle in turn by using a least square method to obtain the curvature radius of each angularr i ；
3) Calculating the roundness n of the sand particles according to formula (1):
in the method, in the process of the invention,r i the radius of curvature of the corner of the particle is indicated,Rindicating the maximum inscribed circle radius of the particles,Nindicating the number of particle edges and corners; and is also provided with
The identification of the sand particle edges and corners comprises edge and corner key point identification, wherein the edge and corner key point identification comprises particle contour smoothing treatment;
the corner key point identification also comprises a particle corner key point mark, which is specifically as follows:
taking 3 adjacent contour coordinate points from the smoothed particle contour as a circle, and marking the middle points of the 3 points as key points of the particle edges and corners if the circle simultaneously meets the following three conditions, namely (a) the circle center is in the particle contour, (b) the radius is smaller than the maximum inscribed circle radius, (c) the circle does not exceed the particle contour;
the identification of the sand particle edges and corners further comprises edge key point grouping, wherein the edge key point grouping refers to dividing the key points into groups according to different edges and corners, the grouping comprises preliminary grouping, and the preliminary grouping adopts a statistical method to set a lengthd f When the distance between two adjacent corner key pointsdLess thand f When the two corner key points are in the same group, otherwise, the two corner key points are in different groups;
in preliminary packetsd f The setting of (2) comprises the following 3 steps:
1) Calculating the distance between two adjacent key points to obtain the maximum distanced max And minimum distanced min ；
2) Calculating the distance normalization value of two adjacent edge key points by using a formula (2)P：
PThe regions of dense value distribution correspond to the angular regions of the particles,Pthe interval with sparse value distribution corresponds to a non-angular area;
3) To further distinguishPThe value is dense interval or sparse interval, and grouping coefficient is introducedaSo thatPE [0, a) is a dense interval,P∈(a,1]the time is a sparse interval, and the calculation is performed by using the formula (3)d f ：
aThe value is obtained by counting the normalized values of two adjacent edge key points of a plurality of particle imagesPIs determined whenPWhen =a, the value is obtained by the formula (2)dNamely, isd f 。
2. The method according to claim 1, characterized in that: in step 200, when different sand particles are distinguished, the sand particles are colored and then image segmentation is performed.
3. The method according to claim 1, characterized in that: in step 300, the obtaining of the sand particle contour pixel in the obtained binary image specifically includes: the background of the binary image is black, particles are white, white connected domains in the image are obtained one by one, each white pixel in each connected domain is traversed, and when black pixels exist in upper, lower, left and right adjacent pixels of the pixel or the pixels are image boundaries, the pixels are judged to be particle contour pixels.
4. The method according to claim 1, characterized in that the particle profile smoothing treatment is in particular:
the first step, sequentially connecting the pixel points of the outline of the sand particles into line segments to form a closed graph, wherein the closed graph is the original outline of the sand particles;
secondly, taking the middle points of all line segments in the original profile of the sand particles, and sequentially connecting the middle points of all line segments into a new profile of the sand particles, wherein the new profile of the sand particles is circulated for 1 time;
thirdly, iterating according to the method of the second step on the basis of calculating the sand particle profile of the second step, so as to obtain a cyclenThe next sand particle profile, until the profile of the sand particle is smooth, exits the cycle.
5. The method according to claim 1, wherein the preliminary grouping result of the particle corner key points is calculated as a corner circle, and the preliminary grouping result of the particle corner key points is finely grouped by a dichotomy when the corner circle calculated by the preliminary grouping exists in one of three cases:
case one: the fitted corner circles exceed the grain boundaries;
and a second case: the fitting optimization of the fitted corner circles is too low;
and a third case: the central angle corresponding to the key point of the edge angle is too small.
6. The method of claim 5, wherein the fine grouping is by dividing the grouping into two groups from a maximum distance within the group, fitting the two groups to circles, respectively; and if the three conditions still exist, repeating the two halves for the new group until the fitted circle does not exist or the number of the grouped points is less than 3.
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