CN114219858A - Three-dimensional rapid positioning method for particles - Google Patents
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Abstract
The invention discloses a three-dimensional rapid positioning method of particles. The method realizes the three-dimensional positioning of the particles at the pixel level according to the distribution condition of the scattering light intensity of the particles in a three-dimensional space and a fast local maximum value search algorithm based on the maximum pooling. The invention provides a rapid method for measuring the three-dimensional distribution of particles in space, has high accuracy and low computational power requirement on a computer, and can be widely used for measuring the three-dimensional distribution and positioning of the particles of bubbles, bacteria, emulsion and solid particles.
Description
Technical Field
The invention relates to the field of microscopic imaging measurement of particles, in particular to a three-dimensional rapid positioning method of particles, and particularly relates to great improvement of positioning speed and accuracy of particles.
Background
The three-dimensional tracing, namely the accurate positioning of the particles, has important significance for researching the dynamic processes of air injection, liquid flow field, emulsion stability, drug particles and microorganisms and other fields. The ever-increasing observation demands of researchers on micro-particles even below the micron mean that a technology for positioning the three-dimensional position of the micro-particles more quickly and accurately so as to obtain the motion state parameters such as the speed of the micro-particles is needed.
At present, common particle dynamic measurement methods include laser speed measurement, particle microscopic tracing and the like. The laser speed measurement is based on Doppler effect, belongs to a single-point speed measurement technology, and cannot provide instantaneous flow speed data of a full field; the micro-tracing of the particles can realize the observation of individual dynamic process and the transient measurement of the whole flow field by tracking and matching each particle in the flow field, but the method is based on a plane fitting method such as a centroid method and the like to position, so that the position coordinates of the particles can be obtained only in a two-dimensional direction, and the micro-tracing of the particles lacks one dimension in the aspect of researching the motion rule of the particles in a three-dimensional space, thereby having great limitation. In the three-dimensional positioning of the particles, the existing method generally obtains the three-dimensional position of the particles according to peak data by performing threshold filtering and fitting of an estimated function on the distribution of a three-dimensional light field, and the fitting process needs large data volume, consumes long time and is influenced by the number of the particles. In addition, a plurality of cameras can be used for collecting tracer particle images under different viewing angles, and then a three-dimensional tracer particle field is reconstructed from the two-dimensional images through an optical tomography algorithm.
Accordingly, there is a need for a fast and convenient three-dimensional positioning method for microparticles to improve the basic problems of high computational requirement, long time consumption, low efficiency, etc. when observing a multi-particle sample, and to promote scientific research in related fields.
Disclosure of Invention
The invention provides a rapid three-dimensional positioning method of particles, which realizes the three-dimensional positioning of the particles at the pixel level according to a rapid local maximum search algorithm based on maximum pooling by analyzing the light intensity space distribution obtained by fluorescent layer scanning imaging or diffraction theory calculation, and is described in detail as follows:
a method for rapid three-dimensional localization of microparticles, characterized in that it comprises the following steps:
1) and acquiring the spatial three-dimensional distribution of the light intensity of the particles, wherein the three-dimensional light field in the step can be a fluorescence field or non-marked bright field imaging. The acquisition mode includes, but is not limited to, using a layer scanning imaging method, such as a confocal fluorescence microscope, to acquire three-dimensional light intensity distribution of particle fluorescence at different heights, or performing three-dimensional light intensity reconstruction on the holographic image according to a diffraction theory to calculate three-dimensional space light intensity distribution at different distances from an imaging plane;
2) finding out a local light intensity maximum point by using a fast local maximum search algorithm based on maximum pooling, and enabling three-dimensional coordinates of the local light intensity maximum point to correspond to the spatial positions of the particles one by one;
the fast local maximum search algorithm specifically comprises the following steps:
in the first step, the side length w of the determination range of the local maximum value is set according to the particle size and the distance between particles. Generally speaking, w is about 2-5 times of the diameter of the particle to be measured when focusing, and the local maximum value judgment can prevent a part of particles from being eliminated due to an overlarge judgment range and prevent a single particle from generating a plurality of positioning positions.
And secondly, calculating pooling conditions. And acquiring the pixel value of the side length of the hologram, and taking the maximum factor smaller than w/2 as the side length p of the pooling kernel. And p is also the step length of the maximum pooling, so that repeated comparison of the same light intensity point is avoided, and the calculation amount is reduced.
And thirdly, performing maximum pooling according to the pooling core. Performing maximum pooling calculation on the light intensity distribution matrix of each layer, setting each layer image as a rectangle with the side length of m x n and the pooling kernel side length of p, dividing each layer image into (m/p) x (n/p) grids with the same size as the pooling kernel, only keeping the numerical value of the maximum point of the numerical value in each grid and the position of the maximum point in the original matrix, and discarding the rest parts. Rearranging the values of the points and the position coordinates of the corresponding original matrix to obtain a matrix of (m x n/p 2) x 4, wherein the four values of each column are respectively from the light intensity value, the x coordinate, the y coordinate and the z coordinate of the reserved points.
And fourthly, further screening the residual points by using an adaptive threshold method. And searching the maximum value and the average value of the light intensity of the residual points, calculating and judging the light intensity threshold value according to the sample, wherein the points lower than the value cannot reflect the space position of the particles, and directly omitting to further reduce the data to be calculated. In general, an appropriate value between 5% and 15% of the maximum light intensity value can be taken as a threshold, and for a part of light fields with great light intensity difference, threshold calculation is required according to the average value of the light fields.
And fifthly, screening the residual points to obtain the point with the maximum local light intensity. And dividing the judgment range of the local maximum value by taking the point to be judged as the center and a preset value as the side length through all unremoved points. And searching all the remaining points in the range, and judging whether the point to be judged is the point with the maximum local light intensity according to the light intensity magnitude relation of the points. All local maximum light intensity points can be obtained through judgment, and the spatial positions of the particles can be reflected by the corresponding three-dimensional coordinates of the points.
3) The spatial distribution of the particles is calculated according to the three-dimensional coordinates of the maximum point of the local light intensity, the corresponding relation is linear, the specific numerical value is related to the microscopic technology for acquiring the light intensity, and the calibration can be carried out according to an actual device during application. For a system capable of continuously acquiring light intensity distribution, three-dimensional space positions of particles can be respectively calculated, and the change of parameters such as the motion direction and the motion speed of the particles on a time dimension can be further acquired by combining parameters such as the space relative position and the motion consistency of the particles.
In the method, for a system capable of continuously acquiring light intensity distribution, three-dimensional spatial positions of particles of the system are respectively calculated, and the variation of parameters such as the motion direction and the motion speed of the particles in a time dimension is further acquired by combining the spatial relative positions and the motion consistency parameters of the particles.
In the method, the local light intensity maximum value is used as a particle positioning basis, and when the particle positioning is carried out, the calculation of the coordinates of each point is independent, so that no error transmission or accumulation exists. In the method, a maximum pooling method and a self-adaptive threshold filtering method are introduced into the fast local maximum search algorithm, so that the occupation of resources required by calculation can be greatly reduced, and the accuracy of the result is not influenced.
In the above method, the maximum pooling applied in the fast local maximum search algorithm in step 2) is not limited to a two-dimensional form, but can be implemented in a higher-dimensional form.
In the method, the judgment range mentioned by the fast local maximum search algorithm is not limited to be square, and the algorithm can also realize the positioning of the local light intensity maximum point under the condition that different geometric models such as a sphere and the like are used as the judgment range.
The technical scheme provided by the invention has the beneficial effects that:
1. the method applies the method of positioning the local maximum light intensity, can automatically set the local maximum judgment range according to the particle size of the sample, and can better adapt to different sample sizes and the amplification rates of the imaging system in practical application;
2. the method applies a method of positioning local light intensity maximum value, has no limitation on the method of obtaining light intensity spatial distribution, has no path dependence when judging the position of the particle, and has universality on data processing;
3. according to the method, a maximum pooling method and a threshold filtering method are introduced in the judgment of the local maximum, so that the calculation speed is greatly increased on the premise of not influencing the calculation result. When the same data is calculated, the time consumption of the method can be reduced to be within one tenth of that of point-by-point analysis;
4. the method introduces a maximum pooling method for calculation, greatly reduces the memory occupation required by calculation, reduces the hardware cost and makes it possible to perform data processing on lighter and cheaper equipment.
5. The method can be conveniently expanded to a higher dimension and can acquire the local maximum point in a special shape range, and has a higher reference meaning for solving special problems.
Drawings
Fig. 1 is a flowchart of a method for fast three-dimensional positioning of particles according to the present invention.
FIG. 2 is a background-subtracted holographic out-of-focus image of Escherichia coli bacteria liquid;
FIG. 3 shows the spatial three-dimensional distribution of E.coli bacterial particles obtained by localization.
FIG. 4 is a holographic defocused image of a PS plastic pellet with a diameter of 0.8 μm, with background subtracted;
fig. 5 shows the three-dimensional distribution of plastic pellet particles obtained by positioning.
FIG. 6 is a background-subtracted holographic out-of-focus image of Pseudomonas aeruginosa PAO1 bacteria liquid;
FIG. 7 shows the three-dimensional distribution of the Pseudomonas aeruginosa bacterial particles obtained by localization.
Detailed Description
The present invention will be described in further detail with reference to examples, but the embodiments of the present invention are not limited thereto.
Example 1
The embodiment of the invention provides an experimental result of three-dimensional positioning of escherichia coli by using a coaxial holographic imaging system, wherein a light source used in the experiment is an LED light source with the wavelength lambda being 505nm, and the magnification of the holographic imaging system is 40 x. And (3) carrying out defocusing holographic imaging on the escherichia coli liquid sample by using a black-and-white camera with the pixel number of 1024 x 1024 and the side length of the pixel point of 6.5 mu m to obtain a graph 2, wherein the graph 2 is subjected to background subtraction.
In consideration of the calculation speed and accuracy, the embodiment of the invention tracks the bacterial particles within a range of 3.5 μm to 63.5 μm from the imaging plane. The distance between adjacent reconstructed light intensity images is calculated and obtained to be 0.1625 mu m according to the side length and the magnification of the pixel, the distance between each layer of reconstructed light intensity surface and the imaging surface is [3.5,3.6625,3.825, …,63.375] by combining the reconstructed distance, the unit is mu m, the distance value is sequentially substituted into a diffraction formula for reconstruction calculation, and a light intensity distribution matrix of 1024 x 370 pixels is obtained.
And performing maximum pooling and threshold filtering on the light intensity distribution matrix. According to practical trial and experience, when the side length w of the local maximum value range is judged to be 70 pixels and the threshold value is 7% of the maximum value of all the light intensity points, the three-dimensional positioning effect of the escherichia coli is the best. The side length of the maximum pooling kernel is smaller than w/2 and is a factor of the image side length, and the pooling kernel side length p is calculated to be 32. And carrying out maximum pooling sampling with a pooling kernel of 32 × 32 on the 1024 × 370 light intensity distribution matrix, wherein the pooling step is 32, and obtaining a filtered light intensity point matrix and a corresponding position thereof, wherein the size of the matrix is 32 × 370. Filtering is carried out by taking 7% of the maximum value of the light intensity point as a threshold value, and points with the light intensity value smaller than the threshold value are cut off. The number of the residual light intensity points in the embodiment of the present invention is 27085, and this part of the points is the possible local maximum light intensity points. And rearranging the obtained residual light intensity points and the position coordinates thereof to obtain an 27085 × 4 matrix, wherein each column of the matrix is the light intensity of the residual light intensity points and the corresponding x coordinate, y coordinate and z coordinate.
And judging the residual points to obtain the real local maximum light intensity point. All light intensity points are marked first, and the initial mark value is 1. And calculating from the first point, if the mark value of the point is 1, judging that the point is possibly the point with the maximum local light intensity, and searching all the residual points with the difference between the horizontal and vertical direction coordinates and the point coordinate being less than w/2 and comparing. And modifying the mark values according to the light intensity value size relationship of the points which meet the conditions, wherein the mark value of the maximum value is unchanged, and the mark values of the rest points are all changed into 0, namely, the points cannot be considered as the local maximum light intensity points. Sequentially judging each subsequent point, if the marking value is 0, comparing the point and determining the point as a non-local maximum light intensity point, and skipping without comparing again; if the flag value is 1, the same determination calculation as the first point needs to be performed. When all the points are judged, the point with the mark value still being 1 is the maximum point of the obtained local light intensity, and the corresponding coordinates can reflect the space position of the thallus particles.
And transforming the three-dimensional coordinates. According to the side length of the pixel point and the magnification of the imaging system, the three-dimensional coordinate unit is converted from the pixel point to the corresponding length unit, so that the three-dimensional positioning of the escherichia coli thallus in the space can be realized, and the spatial distribution condition is shown in fig. 3. Under the condition of applying a GPU acceleration technology, the time consumed for three-dimensional positioning calculation of a single picture is within 2 seconds, and the time can be further shortened by improving hardware and combining technologies such as parallel calculation and the like.
Example 2
The embodiment of the invention provides an experimental result of three-dimensional positioning of PS plastic spheres with the diameter of 0.8 mu m dispersed on the same plane by using a coaxial holographic imaging system, wherein a light source used in the experiment is an LED light source with the wavelength lambda of 450nm, and the magnification of the holographic imaging system is 40 x. And (3) carrying out defocusing holographic imaging on the plastic pellet sample by using a black-and-white camera with the pixel number of 1024 x 1024 and the side length of the pixel point of 6.5 mu m to obtain a graph 4, wherein the graph 4 is subjected to background subtraction.
The embodiment of the invention tracks the image within the range of 3.5 mu m to 63.5 mu m from the imaging surface. The distance between adjacent reconstructed light intensity images is calculated and obtained to be 0.1625 mu m according to the side length and the magnification of the pixel, the distance between each layer of reconstructed light intensity surface and the imaging surface is [3.5,3.6625,3.825, …,63.375] by combining the reconstructed distance, the unit is mu m, the distance value is sequentially substituted into a diffraction formula for reconstruction calculation, and a light intensity distribution matrix of 1024 x 370 pixels is obtained.
And performing maximum pooling and threshold filtering on the light intensity distribution matrix. According to practical trial and experience, when the side length w of the local maximum value range is judged to be 70 pixels and the threshold value is 8% of the maximum value of all the light intensity points, the three-dimensional positioning effect is best. The side length of the maximum pooling kernel is smaller than w/2 and is a factor of the image side length, and the pooling kernel side length p is calculated to be 32. And carrying out maximum pooling sampling with a pooling kernel of 32 × 32 on the 1024 × 370 light intensity distribution matrix, wherein the pooling step is 32, and obtaining a filtered light intensity point matrix and a corresponding position thereof, wherein the size of the matrix is 32 × 370. Filtering is carried out by taking 7% of the maximum value of the light intensity point as a threshold value, and points with the light intensity value smaller than the threshold value are cut off. The number of the residual light intensity points in the embodiment of the present invention is 27085, and this part of the points is the possible local maximum light intensity points. And rearranging the obtained residual light intensity points and the position coordinates thereof to obtain an 27085 × 4 matrix, wherein each column of the matrix is the light intensity of the residual light intensity points and the corresponding x coordinate, y coordinate and z coordinate.
And judging the residual points to obtain the real local maximum light intensity point. All light intensity points are marked first, and the initial mark value is 1. And calculating from the first point, if the mark value of the point is 1, judging that the point is possibly the point with the maximum local light intensity, and searching all the residual points with the difference between the horizontal and vertical direction coordinates and the point coordinate being less than w/2 and comparing. And modifying the mark values according to the light intensity value size relationship of the points which meet the conditions, wherein the mark value of the maximum value is unchanged, and the mark values of the rest points are all changed into 0, namely, the points cannot be considered as the local maximum light intensity points. Sequentially judging each subsequent point, if the marking value is 0, comparing the point and determining the point as a non-local maximum light intensity point, and skipping without comparing again; if the flag value is 1, the same determination calculation as the first point needs to be performed. When all the points are judged, the point with the mark value still being 1 is the maximum point of the obtained local light intensity, and the corresponding coordinates can reflect the space position of the thallus particles.
And transforming the three-dimensional coordinates. According to the side length of the pixel point and the magnification of the imaging system, the three-dimensional coordinate unit is converted from the pixel point to the corresponding length unit, so that the three-dimensional positioning of the plastic pellet in the space can be realized, and the spatial distribution condition is shown in fig. 5. The three-dimensional positions of the plastic balls are basically in the same plane, so that the method is in accordance with the actual sample, and the accuracy of the three-dimensional positioning method can be proved.
Example 3
The embodiment of the invention provides an experimental result of three-dimensional positioning of a pseudomonas aeruginosa PAO1 bacterial liquid sample by using a coaxial holographic imaging system, wherein a light source used in the experiment is an LED light source with the wavelength lambda of 505nm, and the magnification of the holographic imaging system is 40 x. And (3) carrying out defocusing holographic imaging on the bacteria liquid sample by using a black-and-white camera with the pixel number of 1024 x 1024 and the side length of the pixel point of 6.5 mu m to obtain a graph 6, wherein the graph 6 is subjected to background subtraction.
The embodiment of the invention tracks the image within the range of 3.5 mu m to 63.5 mu m from the imaging surface. The distance between adjacent reconstructed light intensity images is calculated and obtained to be 0.1625 mu m according to the side length and the magnification of the pixel, the distance between each layer of reconstructed light intensity surface and the imaging surface is [3.5,3.6625,3.825, …,63.375] by combining the reconstructed distance, the unit is mu m, the distance value is sequentially substituted into a diffraction formula for reconstruction calculation, and a light intensity distribution matrix of 1024 x 370 pixels is obtained.
And performing maximum pooling and threshold filtering on the light intensity distribution matrix. According to practical trial and experience, when the side length w of the local maximum value range is judged to be 70 pixels and the threshold value is 5% of the maximum value of all the light intensity points, the three-dimensional positioning effect is best. The side length of the maximum pooling kernel is smaller than w/2 and is a factor of the image side length, and the pooling kernel side length p is calculated to be 32. And carrying out maximum pooling sampling with a pooling kernel of 32 × 32 on the 1024 × 370 light intensity distribution matrix, wherein the pooling step is 32, and obtaining a filtered light intensity point matrix and a corresponding position thereof, wherein the size of the matrix is 32 × 370. Filtering is carried out by taking 7% of the maximum value of the light intensity point as a threshold value, and points with the light intensity value smaller than the threshold value are cut off. The number of the residual light intensity points in the embodiment of the present invention is 27085, and this part of the points is the possible local maximum light intensity points. And rearranging the obtained residual light intensity points and the position coordinates thereof to obtain an 27085 × 4 matrix, wherein each column of the matrix is the light intensity of the residual light intensity points and the corresponding x coordinate, y coordinate and z coordinate.
And judging the residual points to obtain the real local maximum light intensity point. All light intensity points are marked first, and the initial mark value is 1. And calculating from the first point, if the mark value of the point is 1, judging that the point is possibly the point with the maximum local light intensity, and searching all the residual points with the difference between the horizontal and vertical direction coordinates and the point coordinate being less than w/2 and comparing. And modifying the mark values according to the light intensity value size relationship of the points which meet the conditions, wherein the mark value of the maximum value is unchanged, and the mark values of the rest points are all changed into 0, namely, the points cannot be considered as the local maximum light intensity points. Sequentially judging each subsequent point, if the marking value is 0, comparing the point and determining the point as a non-local maximum light intensity point, and skipping without comparing again; if the flag value is 1, the same determination calculation as the first point needs to be performed. When all the points are judged, the point with the mark value still being 1 is the maximum point of the obtained local light intensity, and the corresponding coordinates can reflect the space position of the thallus particles.
And transforming the three-dimensional coordinates. According to the side length of the pixel point and the magnification of the imaging system, the three-dimensional coordinate unit is converted into a corresponding length unit from the pixel point, so that the three-dimensional positioning of the pseudomonas aeruginosa in the space can be realized, and the spatial distribution condition is shown in fig. 7.
It will be understood by those skilled in the art that the drawings are merely schematic illustrations of preferred embodiments of the present invention, which are not intended to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A method for rapid three-dimensional localization of microparticles, characterized in that it comprises the following steps:
1) acquiring the spatial three-dimensional distribution of the light intensity of the particles or non-marked bright field imaging, wherein the acquisition mode comprises the steps of acquiring the three-dimensional light intensity distribution of the fluorescent particles at different heights by using a layer scanning imaging method, or performing three-dimensional light intensity reconstruction on the holographic image according to a diffraction theory, and calculating the three-dimensional spatial light intensity distribution at different distances from an imaging surface;
2) finding out a local light intensity maximum point by using a fast local maximum search algorithm based on maximum pooling, and enabling three-dimensional coordinates of the local light intensity maximum point to correspond to the spatial positions of the particles one by one;
3) the spatial distribution of the particles is calculated according to the three-dimensional coordinates of the maximum point of the local light intensity, the corresponding relation is linear, the microscopic technology for acquiring the light intensity by specific numerical values is related, and the calibration is carried out according to an actual device during application.
2. The method for rapid three-dimensional localization of particles according to claim 1, wherein in step 1), the three-dimensional light field of the particles is a fluorescence field or a reconstructed three-dimensional light field.
3. The method for rapid three-dimensional localization of particles according to claim 1, wherein in step 1), the layer scan imaging method is layer scan imaging using a confocal fluorescence microscope.
4. The method for fast three-dimensional localization of particles according to claim 1, wherein in step 2), the fast local maximum search algorithm specifically comprises the following steps:
firstly, setting the side length w of a judgment range of a local maximum value according to the size of particles and the distance between the particles; at the moment, the local maximum value judgment can prevent partial particles from being eliminated due to overlarge judgment range and avoid a plurality of positioning positions of a single particle;
secondly, calculating pooling conditions; acquiring a pixel value of the side length of the hologram, and taking a maximum factor smaller than w/2 as the side length p of the pooling kernel; p is also the step length of the maximum pooling, so that repeated comparison of the same light intensity point is avoided, and the calculated amount is reduced;
thirdly, performing maximum pooling according to the pooling core; performing maximum pooling calculation on each layer of light intensity distribution matrix, setting each layer of image as a rectangle with the side length of m x n, setting the side length of a pooling kernel as p, dividing each layer of image into (m/p) x (n/p) grids with the same size as the pooling kernel, only keeping the numerical value of the maximum point of the numerical value in each grid and the position of the maximum point in the original matrix, and discarding the rest parts; rearranging the values and positions of the points to obtain a matrix of m x n/p 2 and a three-dimensional position coordinate of each point in the matrix corresponding to the original matrix;
fourthly, further screening the residual points by using a self-adaptive threshold method; searching the maximum value and the average value of the light intensity of the residual points, calculating and judging a light intensity threshold value according to the sample, wherein points lower than the value cannot reflect the space position of the particles, and directly omitting to further reduce the data to be calculated;
fifthly, screening the residual points to obtain a local maximum light intensity point; dividing a judgment range of a local maximum value by taking a point to be judged as a center and a preset value as a side length through traversing all unremoved points; searching all the remaining points in the range, and judging whether the point to be judged is the local maximum light intensity point or not according to the light intensity magnitude relation of the points; all local maximum light intensity points are obtained through judgment, and the spatial positions of the particles can be reflected by the points corresponding to the three-dimensional coordinates.
5. The method for rapid three-dimensional localization of particles according to claim 4, wherein in the first step, w is 2-5 times the diameter of the particles to be measured when focused.
6. The method of claim 4, wherein in the third step, the intensity values and their corresponding coordinates obtained after the maximum pooling are expressed in a matrix form, and when a matrix of (m x n/p 2) 4 is used, the four values in each column are derived from the intensity value, x-coordinate, y-coordinate and z-coordinate of the retained spot.
7. The method for rapid three-dimensional positioning of particles according to claim 1, wherein in the fourth step, the threshold value is an appropriate value between 5-15% of the maximum value of the light intensity, and for a part of the light field with a great light intensity difference, the average value of the light field is used as a reference, or even the threshold value calculation is performed in different regions.
8. A method for three-dimensional fast localization of particles according to claim 1, wherein in the fifth step, a labeling method is used to avoid repeated comparisons to further speed up the calculation process, i.e. each time a local maximum light intensity point is determined, the points within the range smaller than the value of the central point are labeled and excluded, and in the subsequent calculation these points are not determined again, but are directly identified as non-local maximum light intensity points.
9. The method for fast three-dimensional localization of particles according to claim 1, wherein in step 2), the decision range mentioned by the fast local maximum search algorithm comprises a square or a sphere.
10. The method for rapidly positioning three dimensions of particles according to claim 1, wherein for a system capable of continuously obtaining light intensity distribution, the three-dimensional spatial position of the particles is calculated respectively, and the variation of the parameters such as the motion direction and the motion speed of the particles in the time dimension is further obtained by combining the spatial relative position and the motion consistency parameters of the particles.
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