CN107730513A - A kind of particle recognition and method for tracing based on spheric harmonic function invariant - Google Patents
A kind of particle recognition and method for tracing based on spheric harmonic function invariant Download PDFInfo
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Abstract
The invention belongs to Geotechnical Engineering micro-assay field, and disclose a kind of particle recognition and method for tracing based on spheric harmonic function invariant.This method comprises the following steps：(a) CT scan of particle specimens original state and deformation state, respective CT images figure is obtained；(b) image procossing of CT images figure；(c) three-dimensional configuration of each particle in original state and deformation state CT images figure is characterized using spheric harmonic function；(d) particle under two different conditions is matched by calculating two norm distances of spheric harmonic function invariant, so as to realize the identification of particle.By the present invention, efficiently identify under in situ X-ray diffraction high accuracy CT scan, the sand grains of different load phases, follow the trail of the motor behavior of all sand grains exactly in miniature soil mechanics experiment, applied widely.
Description
Technical Field
The invention belongs to the field of geotechnical engineering miniature tests, and particularly relates to a particle identification and tracking method based on a spherical harmonic invariant.
Background
In recent years, with the intensive research on the complex mechanical behavior of rock-soil dielectric materials, more and more scholars begin to pay attention to the microscopic soil mechanical behavior of soil bodies. Under the background, a discrete element method of a rock-soil advanced numerical simulation technology and a micro soil mechanics test under in-situ X-ray high-precision Computer Tomography (CT) scanning are rapidly developed, and the discrete elements are used for simulating the loading process of a soil body, so that particles can be easily identified and tracked, and the motion behaviors of the particles, such as the displacement, the rotation quantity and the like of the particles, can be obtained. However, the numerical simulation method has a great deal of simplification and hypothesis premises, and cannot truly reflect the complex properties of the geotechnical dielectric materials. Therefore, the research on the micro-mechanics behavior of the soil body by adopting the micro-mechanics test under the in-situ X-ray high-precision CT scanning becomes a necessary trend of the development of the mechanics of the soil. However, unlike discrete element simulation, a key technology in a micro soil mechanics test under CT scanning is to realize the identification and tracking of particles under different loading states, and further obtain the motion behavior of the particles.
To solve this key technology, Ando et al originally proposed a method for identifying and tracking sand grains in a micro triaxial test under CT scanning in 2012. The basic idea is to compare the volumes of sand grains carefully under different loading conditions, and consider that the volumes of the same sand grain are the closest under different loading conditions, however, it should be noted that the number of sand grains is often very large for a sand sample, and the volumes of many sand grains are very close, and in addition, some errors in the volume of the sand grains are caused by the processing procedure of CT images. Therefore, sand grains are identified and tracked from the aspect of volume comparison, the identification result of the sand grains often has a large error, and based on the result, Ando and the like further provide the premise that a sample is divided into a plurality of small search windows and the movement of the sand grains is coordinated to improve the identification efficiency and accuracy of the material consumption.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a particle identification and tracking method based on spherical harmonic invariants, which is characterized by introducing the spherical harmonic invariants of particles to represent the three-dimensional morphological characteristics of the particles, and then compares the second-order norm distances of the spherical harmonic invariants of the particles in different states to quantify the similarity between the particle morphologies, so as to carry out multi-scale matching on the particles, thereby solving the technical problems of low identification accuracy and low applicability of the particles.
To achieve the above object, according to one aspect of the present invention, there is provided a particle identification and tracking method based on a spherical harmonic invariant, the method comprising the steps of:
(a) selecting a stack of particles to prepare a particle sample to obtain a particle sample in an initial state, changing relative positions of the particles in the particle sample to obtain a particle sample in a deformed state, and carrying out CT scanning on the particle sample in the initial state and the particle sample in the deformed state to respectively obtain respective CT image views;
(b) respectively carrying out image processing and analysis on the CT image views in the initial state and the deformation state to obtain the volume, the surface area, the three-dimensional size, the centroid coordinate and the three-dimensional main axis direction of each particle, and meanwhile, respectively numbering each particle in the CT image views in the initial state and the deformation state through different gray values among the particles;
(c) respectively detecting boundary pixels of each particle in the CT image views in the initial state and the deformation state, converting the boundary pixels into three-dimensional coordinates of each vertex forming the particle surface in a space three-dimensional coordinate system according to the resolution of the boundary pixels, converting the three-dimensional coordinates into polar coordinates through coordinate conversion, thereby obtaining the polar coordinates of all the vertices of the particle surface and forming a polar coordinate set, approximating the polar coordinate set by adopting a spherical harmonic sequence, so that each particle represents the three-dimensional surface form of each particle through a spherical harmonic function, thereby enabling each particle in the CT image views in the initial state and the deformation state to form a corresponding spherical harmonic function, and simultaneously calculating the spherical harmonic function invariant corresponding to the spherical harmonic function;
(d) calculating a spherical harmonic invariant second-order norm distance between a particle j in the CT image view in the deformed state and each particle in the CT image view in the initial state one by one, obtaining a particle with the smallest spherical harmonic invariant second-order norm distance from the particle j in the CT image view in the initial state, wherein the particle with the smallest distance is the particle to be identified of the particle j in the initial state, changing the number of the particle j to the number of the particle with the smallest distance, and completing identification of each particle in the CT image view in the deformed state when each particle in the CT image view in the deformed state completes the change of the number, so as to realize identification of the particle, wherein j is 1,2, N, and N is the total number of the particles.
Further preferably, in step (b), the image processing and analyzing comprises: firstly, acquiring a binary image of particles in the CT image view in the initial state and the deformation state, then processing the binary image by adopting a three-dimensional median filter, and finally separating all particles which are mutually contacted in the filtered image by adopting a three-dimensional watershed algorithm.
Further preferably, in step (c), the spherical harmonics preferably take the following expression,
wherein,is related to zenith angle theta and azimuth angle under spherical coordinate systemOf the spherical harmonics, theta ∈ [0, π ∈ ]]，Is the spherical harmonic coefficient corresponding to the nth order m-order term of the spherical harmonic function,is the Legendre polynomial corresponding to the nth order m-order term of the spherical harmonic function.
Further preferably, in step (d), the spherical harmonic invariants are preferably expressed by the following expressions
Wherein,is a spherical harmonic functionIs not changed in the above-mentioned manner,is the second-order norm of the nth order of the spherical harmonics,is a spherical harmonic functionFrequency components of nth order.
Further preferably, in step (d), the spherical harmonics invariant second order norm distance preferably takes the following expression,
where SH (f) is the invariant of spherical harmonics of the particles in the initial state, SH (g) is the invariant of spherical harmonics of the particles in the deformed state, | fnI is the second-order norm of the nth order of the spherical harmonic function of the particle in the initial state, gnAnd | | is the second-order norm of the nth order of the spherical harmonic function of the particle in a deformed state.
Further preferably, in step (c), the maximum order of the spherical harmonics is selected to be 15.
Further preferably, after the particle identification is completed, the centroid and the main axis direction of the particle in the initial state and the deformation state are respectively obtained, and the change of the centroid and the main axis direction in the initial state and the deformation state is the particle motion behavior, so that the tracking of the particle motion behavior is realized.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. the three-dimensional morphological characteristics of the particles are represented by introducing the spherical harmonic invariants of the particles, the similarity between the particle morphologies is quantified by comparing the second-order norm distances of the spherical harmonic invariants of the particles in different states, and then the particles are subjected to multi-scale matching, so that the sand grains in different loading states are identified in the micro soil mechanics test under high-precision CT scanning, the accuracy and the applicability of the identification method are improved, and the identification method is suitable for various micro soil mechanics tests under large deformation conditions;
2. the particle identification and tracking technology provided by the invention effectively identifies sandy soil particles at different loading stages in a micro soil mechanics test under in-situ X-ray high-precision CT scanning, further accurately tracks the motion behaviors of all the sandy soil particles, such as displacement, rotation amount and the like, and is particularly suitable for soil mechanics tests under large deformation conditions, such as single shear test, ring shear test and the like;
3. the identification method provided by the invention has the advantages of simple steps and strong applicability, can accurately and quickly identify the deformed particles, can accurately track the movement behaviors of the particles by calculating the mass centers and the main shaft directions of the particles in different states after the particles are successfully identified, and has wide application range.
Drawings
FIG. 1 is a flow chart of particle identification and tracking constructed in accordance with a preferred embodiment of the present invention;
FIG. 2(a) is a schematic illustration of selected sand particles constructed in accordance with a preferred embodiment of the present invention;
FIG. 2(b) is a schematic illustration of a prepared particle sample constructed in accordance with a preferred embodiment of the present invention;
FIG. 2(c) is a schematic illustration of a particle sample being placed on a scanning platform constructed in accordance with a preferred embodiment of the present invention;
FIG. 2(d) is a process of X-ray CT scanning of a particle sample constructed in accordance with a preferred embodiment of the present invention;
FIG. 3 is a CT image view of a particle sample constructed in accordance with a preferred embodiment of the present invention in an initial state and in a deformed state;
FIG. 4(a) is a CT image of a particle sample constructed in accordance with a preferred embodiment of the present invention;
FIG. 4(b) is a binarized image of a CT image of a grain sample constructed in accordance with a preferred embodiment of the present invention;
FIG. 4(c) is a three-dimensional median filtered image of FIG. 4(b) constructed in accordance with a preferred embodiment of the present invention;
FIG. 4(d) is an image constructed in accordance with a preferred embodiment of the present invention after separating the contacted particles using a three-dimensional watershed algorithm with respect to FIG. 4 (c);
FIG. 5(a) is a CT sample influence graph of particles constructed in accordance with a preferred embodiment of the present invention;
FIG. 5(b) is a reconstructed particle morphology using superposition of 15 order frequency components constructed in accordance with a preferred embodiment of the present invention;
FIG. 5(c) is a 0 th order spherical harmonic constructed in accordance with a preferred embodiment of the present invention;
FIG. 5(d) is a particle morphology of 2-4 spherical harmonics constructed in accordance with a preferred embodiment of the present invention;
FIG. 5(e) is a particle morphology of order 5-8 spherical harmonics constructed in accordance with a preferred embodiment of the present invention;
FIG. 5(f) is a particle morphology of spherical harmonics of order 9-15 constructed in accordance with a preferred embodiment of the present invention;
FIG. 6 is a block diagram of a particle recognition technique of the present invention for recognizing two states of sand constructed in accordance with a preferred embodiment of the present invention;
fig. 7 illustrates the amount of displacement and rotation tracked from an initial state to a deformed state for a particle constructed in accordance with a preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Fig. 1 is a flow chart of particle identification and tracking constructed according to a preferred embodiment of the present invention, and as shown in fig. 1, detailed implementation procedures of specific steps according to a preferred embodiment of the present invention are as follows:
(1) CT scanning of sandy soil samples
Performing X-ray CT scanning on different states of a sandy soil sample, wherein fig. 2(a) is a schematic diagram of selected sandy soil particles constructed according to a preferred embodiment of the present invention, fig. 2(b) is a schematic diagram of a prepared particle sample constructed according to a preferred embodiment of the present invention, fig. 2(c) is a schematic diagram of a particle sample placed on a scanning platform constructed according to a preferred embodiment of the present invention, and fig. 2(d) is an X-ray CT scanning process of the particle sample constructed according to a preferred embodiment of the present invention, as shown in fig. 2(a) to (d), firstly, randomly selecting a pile of sand grains between 1mm and 2mm as a research object (as shown in fig. 2 (a)); loading all sand grains into a polycarbonate plastic casing with an inner diameter of phi 10mm and a height of 12mm for sample preparation, and fixing with silica gel oil (as shown in FIG. 2 (b)); fixing the manufactured sandy soil sample on a rotary bracket suitable for a scanning platform of a CT system (as shown in figure 2 (c)); and then the CT system is placed under an X-ray source of the CT system to complete a 360-degree CT scan, and the imaging of the CT is completed on a detector at the back (as shown in fig. 2 (d)). The CT scan of the initial sample is taken as the reference state. And then, stirring the sand grains in the casing by using a steel nail, simulating a large deformation state of the sand under a ring shear test, and finishing CT scanning and CT imaging of 360 degrees once again. Fig. 3 is a CT image of a particle sample constructed according to a preferred embodiment of the present invention in an initial state and in a deformed state, as shown in fig. 3, where it can be noted that all sand grains are greatly displaced and rotated. Therefore, the particles of the sample in the deformed state need to be identified according to the particle number of the sample in the initial state, so as to track the motion behavior of the sample.
(2) Processing and analysis of CT images
Fig. 4(a) is a CT image of a grain sample constructed according to a preferred embodiment of the present invention, fig. 4(b) is a binarized image of the CT image of the grain sample constructed according to the preferred embodiment of the present invention, fig. 4(c) is a three-dimensional median filtered image of fig. 4(b) constructed according to the preferred embodiment of the present invention, fig. 4(d) is an image of fig. 4(c) separated from the contacted grains by using a three-dimensional watershed algorithm, as shown in fig. 4(a), showing an original CT image including four phases of carbonate plastic casing, silicone oil, sand and air, the present invention mainly performs image processing by means of open-source image processing software ImageJ, first, filtering off the acid ester plastic casing and the silicone oil phase by using threshold value processing, obtaining a binarized image containing only the sand phase, where the gray value of the sand pixels is 256 and the gray value of the background pixels is 0, see fig. 4 (b); because some noisy pixels exist in the CT image after binarization processing, a three-dimensional median filter is adopted for processing, and the filtering intensity is 5 pixels, as shown in a figure 4 (c); finally, all contacted particles are separated using a three-dimensional watershed algorithm, and each particle is numbered using a series of consecutive gray values, see fig. 4 (d).
(3) Spherical harmonic analysis of particle morphology
Based on the processed CT image, for a certain single sand grain, the contained pixel volume element can be quickly identified through the gray number of the sand grain. And detecting boundary pixels of the particles by adopting a boundary pixel searching algorithm in ImageJ, and converting according to the pixel resolution to obtain a group of vertex coordinate sets V (x, y, z) forming the surfaces of the particles. The invention adopts the ball coordinate transformation to obtain the polar coordinate set of the sand outline, and then adopts the three-dimensional spherical harmonic function sequence to reconstruct the three-dimensional surface morphology of the sand, the basic idea is to expand the polar coordinate set of a unit ball to the polar coordinate set corresponding to the actual sand through the approximation of the spherical harmonic function sequence, and obtain the corresponding spherical harmonic coefficient, as follows:
in the formula, theta is belonged to 0, pi]Andrespectively representing zenith and azimuth angles of the spherical coordinate system. Wherein,is an nth order m-th base of the spherical harmonic function, determined by formula (2),is its corresponding spherical harmonic coefficient.
In the formula,is the associated legendre polynomial. Wherein n is an integer from 0 to positive infinity, the specific value is determined by the reconstruction accuracy of the sand grains, and a group of spherical harmonic coefficientsTotal number of (n +1)2。
Substituting the existing surface polar coordinate set into the formula (1) to obtain an unknown number (n +1)2According to a large amount of spherical harmonic analysis, the linear equation system of the natural sand can be well fitted with the three-dimensional morphological characteristics of the natural sand grains when the maximum order adopts 15,therefore, the maximum order n of the spherical harmonic function adopted in the inventionmaxThis set of spherical harmonic coefficients can be found using a least squares estimation, 15. Based on the fundamental properties of spherical harmonics, the present invention introduces a set of spherical harmonic invariants, i.e., energies of frequency components of different orders of spherical harmonics, to characterize the multi-scale features of particle morphology, as shown in equation 3 below.
In the formula,representsThe frequency components at different orders can be expressed as:
the two-norm of (a) can be calculated by the following formula:
FIG. 5(a) is a CT sample influence graph of a particle constructed according to a preferred embodiment of the present invention, FIG. 5(b) is a particle morphology reconstructed by superposition of 15-order frequency components constructed according to a preferred embodiment of the present invention, FIG. 5(c) is a 0-order spherical harmonic constructed according to a preferred embodiment of the present invention, FIG. 5(d) is a particle morphology of 2-4-order spherical harmonics constructed according to a preferred embodiment of the present invention, FIG. 5(e) is a particle morphology of 5-8-order spherical harmonics constructed according to a preferred embodiment of the present invention, FIG. 5(f) is a particle morphology of 9-15-order spherical harmonics constructed according to a preferred embodiment of the present invention, and as shown in FIGS. 5(a) - (f), it can be seen that the particle morphology reconstructed by superposition of 15-order frequency components (FIG. 5(b)) substantially coincides with its CT image (FIG. 5(a)), wherein the 0-order frequency component represents the volume size of the particles (fig. 5 (c)); the 2-4 order frequency components represent the general morphology of the particles (FIG. 5 (d)); the 5-8 th order represents the local angular characteristics of the particles (FIG. 5 (e)); steps 9 to 15 represent the texture features of the particle surface (FIG. 5 (f)).
(4) Multi-scale matching algorithm for particle morphology
In order to evaluate the similarity between different particle morphologies, the present invention provides a method for comprehensively comparing the multi-scale morphological characteristics of particles, i.e. quantifying the morphological differences according to the second-order norm distance of the 15 th-order spherical harmonic invariants between particles, as shown in the following formula:
in the formula, f and g represent the spherical harmonics of a particle in the initial state and the spherical harmonics of a particle in the deformed state, respectively.
Through the detailed calculation of the second-order norm distance of the spherical harmonic invariants between the particles in the two states, the two particles are considered to be two states of the same particle when the norm distance between the two particles is the minimum. Fig. 6 is a block diagram of a method for identifying particles in two states of sand using the particle recognition technique of the present invention, as shown in fig. 6, wherein the same color represents the same particle in the two states. The accuracy of the recognition result is very good by visual inspection. Further examination shows that the accuracy of the particle identification by adopting the method of the invention reaches 98 percent, while the accuracy of the traditional volume comparison identification method is only 26 percent. Therefore, it can be shown that the conventional method is not suitable for the particle recognition of the sample under the large deformation, and the method of the invention is well suitable for the particle recognition of the sample under the large deformation.
After the particles are successfully identified, the motion behaviors of the particles can be accurately tracked by calculating the mass centers and the main axis directions of the particles under different states. FIG. 7 shows the amount of displacement and rotation tracked from the initial state to the deformed state of the same pellet constructed according to the preferred embodiment of the present invention, as shown in FIG. 7, wherein the initial state centroid of the pellet has coordinates of (1.48mm, 1.33mm, 1.89mm), (81 degrees, 131 degrees) in the three-dimensional space coordinate and the spherical coordinate system, respectively, and the centroid of the pellet has coordinates of (1.56mm, 1.59mm, 1.72mm), (63 degrees, 155 degrees) in the three-dimensional space coordinate and the spherical coordinate system, respectively, such that the pellet moves with displacement of (0.08mm, 0.26mm, -0.17mm) and rotation angle of (-18 degrees, 24 degrees)
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A method for identifying and tracking particles based on invariant spherical harmonics, the method comprising the steps of:
(a) selecting a stack of particles to prepare a particle sample to obtain a particle sample in an initial state, changing relative positions of the particles in the particle sample to obtain a particle sample in a deformed state, and carrying out CT scanning on the particle sample in the initial state and the particle sample in the deformed state to respectively obtain respective CT image views;
(b) respectively carrying out image processing and analysis on the CT image views in the initial state and the deformation state to obtain the volume, the surface area, the three-dimensional size, the centroid coordinate and the three-dimensional main axis direction of each particle, and meanwhile, respectively numbering each particle in the CT image views in the initial state and the deformation state through different gray values among the particles;
(c) respectively detecting boundary pixels of each particle in the CT image views in the initial state and the deformation state, converting the boundary pixels into three-dimensional coordinates of each vertex forming the particle surface in a space three-dimensional coordinate system according to the resolution of the boundary pixels, converting the three-dimensional coordinates into polar coordinates through coordinate conversion, thereby obtaining the polar coordinates of all the vertices of the particle surface and forming a polar coordinate set, approximating the polar coordinate set by adopting a spherical harmonic sequence, so that each particle represents the three-dimensional surface form through a spherical harmonic function, thereby enabling each particle in the CT image views in the initial state and the deformation state to form a corresponding spherical harmonic function, and simultaneously obtaining a corresponding spherical harmonic function invariant through the spherical harmonic function;
(d) calculating a spherical harmonic invariant second-order norm distance between a particle j in the CT image view in the deformed state and each particle in the CT image view in the initial state one by one, obtaining a particle with the smallest spherical harmonic invariant second-order norm distance from the particle j in the CT image view in the initial state, wherein the particle with the smallest distance is the particle to be identified of the particle j in the initial state, changing the number of the particle j to the number of the particle with the smallest distance, and completing identification of each particle in the CT image view in the deformed state when each particle in the CT image view in the deformed state completes the change of the number, so as to realize identification of the particle, wherein j is 1,2, N, and N is the total number of the particles.
2. The method for identifying and tracking particles based on invariant spherical harmonics according to claim 1, wherein in step (b), said image processing and analyzing comprises: firstly, acquiring a binary image of particles in the CT image view in the initial state and the deformation state, then processing the binary image by adopting a three-dimensional median filter, and finally separating all particles which are mutually contacted in the filtered image by adopting a three-dimensional watershed algorithm.
3. The method for identifying and tracking particles based on invariant of spherical harmonics according to claim 1 or 2, wherein in step (c), said spherical harmonics preferably adopt the following expressions,
wherein,is related to zenith angle theta and azimuth angle under spherical coordinate systemOf the spherical harmonics, theta ∈ [0, π ∈ ]]， Is the spherical harmonic coefficient corresponding to the nth order m-order term of the spherical harmonic function,is the Legendre polynomial corresponding to the nth order m-order term of the spherical harmonic function.
4. A method for identifying and tracking particles based on spherical harmonic invariants as claimed in any one of claims 1 to 3, wherein in step (d), said spherical harmonic invariants are preferably expressed as follows
Wherein,is a spherical harmonic functionIs not changed in the above-mentioned manner,is the second-order norm of the nth order of the spherical harmonics,is a spherical harmonic functionFrequency components of nth order.
5. A method for identifying and tracking particles based on spherical harmonic invariants as claimed in any one of claims 1 to 4, wherein in step (d), the second-order norm distance of the spherical harmonic invariants preferably adopts the following expression,
<mrow> <mo>|</mo> <mo>|</mo> <mi>S</mi> <mi>H</mi> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>S</mi> <mi>H</mi> <mrow> <mo>(</mo> <mi>g</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msup> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>f</mi> <mi>n</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>-</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>g</mi> <mi>n</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>
where SH (f) is the invariant of spherical harmonics of the particles in the initial state, SH (g) is the invariant of spherical harmonics of the particles in the deformed state, | fnI is the second-order norm of the nth order of the spherical harmonic function of the particle in the initial state, gnAnd | | is the second-order norm of the nth order of the spherical harmonic function of the particle in a deformed state.
6. A method for identifying and tracking particles based on invariant spherical harmonics according to any of claims 1-5 and wherein in step (c) said spherical harmonics have a maximum order of 15.
7. The method for identifying and tracking particles based on the invariant of spherical harmonics according to any one of claims 1-6, wherein after the particle identification is completed, the directions of the centroid and the principal axis of the particle in the initial state and the deformation state are respectively obtained, and the changes of the directions of the centroid and the principal axis in the initial state and the deformation state are the particle motion behaviors, thereby realizing the tracking of the particle motion behaviors.
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