CN102930526A - Space polar coordinate based particle three-dimensional motion matching method - Google Patents

Abstract

The invention belongs to the field of multiphase flow three-dimensional measurement, and provides a space polar coordinate based particle three-dimensional motion matching method for performing exact and efficient three-dimensional motion matching on continuous multi-frame particle images acquired in an unsteady multiphase flow field. The technical scheme adopted by the invention is that the space polar coordinate based particle three-dimensional motion matching method comprises the steps of: extracting a two-dimensional center-of-mass coordinate of each particle in different perspectives at the same moment based on particle regional characteristics; determining a corresponding relationship of the same particle in the different perspectives; calculating to obtain a three-dimensional center-of-mass coordinate of a particle in a single-frame image by combining calibration parameters of a standard field and a three-dimensional measurement model; setting a spherical search window by regarding three-dimensional characteristic parameters of the particle; establishing a space polar coordinate system; and respectively obtaining projection angles of the coordinate system in the three axial directions so as to uniquely determine a space point of motion of the same particle in the multi-frame image. The space polar coordinate based particle three-dimensional motion matching method, disclosed by the invention, is mainly applied to multiphase flow three-dimensional measurement.

Description

Particle three-dimensional motion match method based on space polar coordinate

Technical field

The invention belongs to polyphasic flow three-dimensional measurement field, particularly a kind of particle three-dimensional motion match method based on space polar coordinate.

Background technology

Polyphasic flow is ubiquitous phenomenon among nature and the human lives, has all obtained increasingly extensive application at numerous areas such as water conservancy, the energy, environmental protection, machineries, has important researching value.In order to further investigate Multiphase Flow mechanism, accurately explain the kinetic characteristic of disperse phase, need to carry out three-dimensional measurement to the characteristic parameter of broad sense particle in the polyphasic flow (bubble, drop, solid particle etc.), such as three-dimensional track, velocity field etc.The tracking of particle and motion match are indispensable key links during particle three-dimensional is measured, and in order to determine same particle residing movement position in successive frame, judge the dynamic corresponding relation of each particle in the continuous multiple frames image.

For Particles Moving coupling in the polyphasic flow, typical method has iterative estimation method based on matching probability, neural network matching algorithm, ant colony optimization algorithm and based on the Particles Moving characteristics algorithm etc.First three class algorithm is based on the specific mathematical model, precision height but arithmetic speed is slow.Based on the matching algorithm of Particles Moving feature according to Particles Moving situation setting search scope, in conjunction with particular constraints condition locking coupling particle, higher and the fast operation of precision, but these class methods are applied to testing the speed and following the tracks of of two dimensional image flow field particle mostly at present, do not take into full account the objective attribute of Space Particle three-dimensional motion.Based on Stereo Vision Measurement System, such as two or many three-dimension measuring systems that high-speed camera is set up, or the virtual three-dimensional three-dimension measuring system of separate unit high-speed camera and respective optical system foundation, can realize the information fusion of Double-visual angle measuring object, reflect better the particle three-dimensional kinetic characteristic, and analyse in depth its each phase flow mechanism.Therefore, how to realize the three-dimensional motion coupling of polyphasic flow particle picture under the three-dimension measuring system, become the major issue that needs to be resolved hurrily in particle characteristics parameter three-dimensional measurement and the reconstruction.

Summary of the invention

The present invention is intended to overcome the deficiencies in the prior art, particle three-dimensional motion match method based on space polar coordinate is provided, thereby the continuous multiple frames particle picture that gathers in the non-steady heterogeneous flow field is carried out accurately, three-dimensional motion is mated effectively, for achieving the above object, the technical scheme that the present invention takes is, particle three-dimensional motion match method based on space polar coordinate, comprise the following steps: utilizing the three-dimensional measurement platform to obtain on the basis of Double-visual angle particle original image, by Digital Image Processing, according to the particle provincial characteristics, extract the two-dimentional center-of-mass coordinate of each particle in the synchronization different visual angles, based on how much of polar curves and particle property constraint condition, determine the corresponding relation of same particle in different visual angles, simultaneously in conjunction with accurate on-site proving parameter and three-dimensional measurement model, calculate the three-dimensional center-of-mass coordinate of particle in the single-frame images, with the particle three-dimensional characteristic parameter as matching characteristic, set spherical query window, set up space polar coordinate system, ask for respectively the projection angle of coordinate system on three direction of principal axis, and in conjunction with the threshold value constraint of space utmost point footpath distance, thereby uniquely determine the spatial point that same particle moves in multiple image.

Described step further is refined as:

1, the continuous multiple frames Double-visual angle particle picture to obtaining utilizes digital image processing techniques, extracts the two-dimentional center-of-mass coordinate of each particle, according to existing calibrating parameters and measurement model, calculates the three-dimensional center-of-mass coordinate of each particle;

2, in the first two field picture, point centered by particle barycenter to be matched is set spherical query region take the maximum range value of interframe Particles Moving as radius, and other particles in the zone are its neighbor point, set up space polar coordinate system take central point as initial point;

3, in the second two field picture, may with particle to be matched in the first frame be same particle be called candidate's particle, its barycenter is candidate point, centered by candidate point, offer equally the spherical query window identical with the first frame radius value, and set up corresponding space polar coordinate system, the neighbor point that other particle barycenter in the query region are candidate point;

4, respectively in the first frame and the second two field picture, calculate the space utmost point footpath distance value of each neighbor point and central point and the projection angle of three change in coordinate axis direction, and the calculated value apart from calculated value and three angles of each neighbor point in the first frame and the second frame compared, and setting threshold constraint;

5, definition similarity coefficient objective function, each candidate point in the second frame can draw a corresponding similarity coefficient, and satisfies the candidate point that threshold condition is at most the similarity coefficient maximum, and being with particle to be matched is the motion match point of same particle.

The three-dimensional center of mass point of each particle is set spherical query window radius R in obtaining continuous two width of cloth images _hThreshold value is the largest motion distance, delta d that is not less than particle _Max, generally get R _h=Δ d _Max

Suppose that the two continuous frames image is respectively i frame and i+1 frame, then in the i two field picture, take particle three-dimensional center of mass point m to be matched as the centre of sphere, R _hFor radius is made a spherical query region, the volume coordinate of some m is

Except a m, also have K particle in this zone, be called the neighbor point of a m, with m _kExpression (k=1 ..., K), its volume coordinate is respectively

Take a m as initial point, set up space polar coordinate system, then the relation of other neighbor points and m can be by space utmost point footpath in the i two field picture

With three axial projection angles

Next unique definite, wherein

$r_{\mathrm{mk}}^i=\sqrt{{(x_{\mathrm{mk}}^i-x_m^i)}^2+{(y_{\mathrm{mk}}^i-y_m^i)}^2+{(z_{\mathrm{mk}}^i-z_m^i)}^2}---\left(1\right)$

${\mathrm{\θ}}_{\mathrm{mkx}}^i=\arcsin \frac{x_{\mathrm{mk}}^i-x_m^i}{r_{\mathrm{mk}}^i},$ ${\mathrm{\θ}}_{\mathrm{mky}}^i=\arcsin \frac{y_{\mathrm{mk}}^i-y_m^i}{r_{\mathrm{mk}}^i},$ ${\mathrm{\θ}}_{\mathrm{mkz}}^i=\arcsin \frac{z_{\mathrm{mk}}^i-z_m^i}{r_{\mathrm{mk}}^i}---\left(2\right)$

In the i+1 two field picture, may with particle to be matched in the i frame be same particle be referred to as candidate's particle, its center of mass point is candidate point, represents with n.For a n, offering equally the Radius value is R _hSpherical query window, and set up corresponding space polar coordinate, wherein n _g(g=1 ..., G) being the neighbor point of candidate point, G is the number of neighbor point, the space utmost point directly is three Individual axial projection angle is respectively

According to i frame and i+1 frame hollow compole footpath and projection angle value definition similarity coefficient function S _Mn:

$S_{\mathrm{mn}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{g=1}{\overset{G}{\mathrm{\Σ}}}H({\mathrm{\ϵ}}_r-|r_{\mathrm{mk}}^i-r_{\mathrm{ng}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θx}}-|{\mathrm{\θ}}_{\mathrm{mkx}}^i-{\mathrm{\θ}}_{\mathrm{ngx}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θy}}-|{\mathrm{\θ}}_{\mathrm{mky}}^i-{\mathrm{\θ}}_{\mathrm{ngy}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θz}}-|{\mathrm{\θ}}_{\mathrm{mkz}}^i-{\mathrm{\θ}}_{\mathrm{ngz}}^{i+1}\left|\right)---\left(3\right)$

Wherein, H (r, θ _x, θ _y, θ _z) be step function:

$H(r,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)=\left\{\begin{array}{cc}1,& r>0,{\mathrm{\θ}}_x>0,{\mathrm{\θ}}_y>0\mathrm{and}{\mathrm{\θ}}_z>0;\\ 0,& \mathrm{otherwise}...\end{array}\right.,---\left(4\right)$

ε _rBe the threshold value in space utmost point footpath, value is less than 5 pixels usually; ε _{θ x}, ε _{θ y}And ε _{θ z}Be respectively the setting threshold of three direction of principal axis projection angles, value is less than 30 ° usually; For candidate's particle point that each m in the i+1 two field picture is ordered, can be according to objective function S _MnObtain a similarity coefficient, the point of similar value maximum wherein, being with particle center of mass point m to be matched is the match point of same particle.

The present invention is by setting particle three-dimensional matching characteristic and spherical query window, set up space polar coordinate system, according to the utmost point footpath of adjacent particles center-of-mass coordinate point in the hunting zone and the polar angle of three directions, define and calculate the similarity coefficient objective function of each point, choose the maximum and be the coupling particle, thereby realized the accurate coupling of continuous multiple frames particle picture in the three-dimension measuring system, for follow-up particle three-dimensional movement locus is rebuild and the space establish a firm foundation that tests the speed.

Description of drawings

Fig. 1 is particle picture collection and the three-dimension measuring system based on two high-speed cameras.

Fig. 2 is particle picture collection and the three-dimension measuring system based on the separate unit high-speed camera.

Fig. 3 is the particle three-dimensional motion match method synoptic diagram based on space polar coordinate.

Fig. 4 is particle sequence image (take many bubbles as example).

Fig. 5 is Particles Moving coupling and track reconstructing result (take many bubbles as example).

Embodiment

The motion match of broad sense particle (bubble, drop, solid particle) in the polyphasic flow characteristic parameter three-dimensional measurement platform that this method is applicable to form based on two high-speed cameras equally also is applicable to the motion match based on particle picture in the virtual three-dimensional measuring table of separate unit high-speed camera and respective optical system (such as the refractive power light splitting optical path) composition.

Utilizing the three-dimensional measurement platform to obtain on the basis of Double-visual angle particle original image, by Digital Image Processing, according to the particle provincial characteristics, extract the two-dimentional center-of-mass coordinate of each particle in the synchronization different visual angles, based on constraint conditions such as how much of polar curves and particle properties, determine the corresponding relation of same particle in different visual angles, simultaneously in conjunction with accurate on-site proving parameter and three-dimensional measurement model, can calculate the three-dimensional center-of-mass coordinate of particle in the single-frame images.In order to strengthen the adaptation for the particle three-dimensional kinetic characteristic, the present invention with the particle three-dimensional characteristic parameter as matching characteristic, set spherical query window, set up space polar coordinate system, the break the normal procedure constraint of utmost point footpath and single polar angle, ask for respectively the projection angle of coordinate system on three direction of principal axis, and in conjunction with the threshold value constraint of space utmost point footpath distance, thereby uniquely determine the spatial point that same particle moves in multiple image.

Concrete matching process is as follows:

1, the continuous multiple frames Double-visual angle particle picture to obtaining utilizes digital image processing techniques, extracts the two-dimentional center-of-mass coordinate of each particle, according to existing calibrating parameters and measurement model, calculates the three-dimensional center-of-mass coordinate of each particle;

2, in the first two field picture, point centered by particle barycenter to be matched is set spherical query region take the maximum range value of interframe Particles Moving as radius, and other particles in the zone are its neighbor point, set up space polar coordinate system take central point as initial point;

3, in the second two field picture, may with particle to be matched in the first frame be same particle be called candidate's particle, its barycenter is candidate point, centered by candidate point, offer equally the spherical query window identical with the first frame radius value, and set up corresponding space polar coordinate system, the neighbor point that other particle barycenter in the query region are candidate point;

4, respectively in the first frame and the second two field picture, calculate the space utmost point footpath distance value of each neighbor point and central point and the projection angle of three change in coordinate axis direction, and the calculated value apart from calculated value and three angles of each neighbor point in the first frame and the second frame compared, and setting threshold constraint;

5, definition similarity coefficient objective function, each candidate point in the second frame can draw a corresponding similarity coefficient, and satisfies the candidate point that threshold condition is at most the similarity coefficient maximum, and being with particle to be matched is the motion match point of same particle.

The invention provides a kind of particle three-dimensional motion match method based on space polar coordinate, the method takes into full account the spatial movement characteristic of particle, based on space polar coordinate, determined the motion match method take the particle three-dimensional center of mass point as matching characteristic, take spherical solid space as the region of search.

The present invention is described further below in conjunction with accompanying drawing.

Illustrated in figures 1 and 2 is particle three-dimensional image acquisition and measuring system.Wherein Fig. 1 is particle collection and the three-dimension measuring system based on two high-speed cameras, and two high-speed cameras cross, symmetry is put, and gathers the polyphasic flows particle picture and mates and three-dimensional reconstruction from two different visual angles; Fig. 2 is particle collection and three-dimension measuring system (consisting of example with the refractive power beam-splitting optical system) based on the separate unit high-speed camera, and wherein C is the entity high-speed camera, through two groups of catoptron group P ₁, P ₂And M ₁, M ₂Virtual is left and right virtual video camera C _L, C _R, obtain on this basis the Double-visual angle particle picture of polyphasic flow and mate and three-dimensional reconstruction.The particle picture three-dimensional motion that patent of the present invention is applicable to gather in the above two class platforms is mated.

Figure 3 shows that the particle three-dimensional motion match method synoptic diagram based on space polar coordinate, it is according to the two continuous frames image that gathers gained, utilize coupling particle three-dimensional barycenter and the space length between other particle barycenter and projection angle concern on every side, set up the similarity objective function and mate and follow the tracks of, do further detailed explanation below in conjunction with this figure.

The three-dimensional center of mass point of each particle in obtaining continuous two width of cloth images (representing with " * " among the figure), then candidate's particle of particle to be matched in the first width of cloth image will be arranged in the second width of cloth image take particle to be matched as the center of circle, in certain spheric region that radius is fixed.According to equipment constant frame period Δ t and measured particle maximum movement speed Δ v _Max, can obtain the largest motion distance, delta d of successive frame particle _Max, thus, set spherical query window radius R _hThreshold value is the largest motion distance, delta d that is not less than particle _Max, generally get R _h=Δ d _Max

Suppose that the two continuous frames image is respectively i frame and i+1 frame, then in the i two field picture, take particle three-dimensional center of mass point m to be matched as the centre of sphere, R _hFor radius is made a spherical query region, the volume coordinate of some m is

Except a m, also have K particle in this zone, be called the neighbor point of a m, with m _kExpression (k=1 ..., K), its volume coordinate is respectively

Take a m as initial point, set up space polar coordinate system, then the relation of other neighbor points and m can be by space utmost point footpath in the i two field picture

With three axial projection angles

Next unique definite, wherein

$r_{\mathrm{mk}}^i=\sqrt{{(x_{\mathrm{mk}}^i-x_m^i)}^2+{(y_{\mathrm{mk}}^i-y_m^i)}^2+{(z_{\mathrm{mk}}^i-z_m^i)}^2}---\left(1\right)$

${\mathrm{\θ}}_{\mathrm{mkx}}^i=\arcsin \frac{x_{\mathrm{mk}}^i-x_m^i}{r_{\mathrm{mk}}^i},$ ${\mathrm{\θ}}_{\mathrm{mky}}^i=\arcsin \frac{y_{\mathrm{mk}}^i-y_m^i}{r_{\mathrm{mk}}^i},$ ${\mathrm{\θ}}_{\mathrm{mkz}}^i=\arcsin \frac{z_{\mathrm{mk}}^i-z_m^i}{r_{\mathrm{mk}}^i}---\left(2\right)$

In the i+1 two field picture, may with particle to be matched in the i frame be same particle be referred to as candidate's particle, its center of mass point is candidate point, represents with n.For a n, offering equally the Radius value is R _hSpherical query window, and set up corresponding space polar coordinate, wherein n _g(g=1 ..., G) being the neighbor point of candidate point, G is the number of neighbor point, the space utmost point directly is three

Individual axial projection angle is respectively

According to i frame and i+1 frame hollow compole footpath and projection angle value definition similarity coefficient function S _Mn:

$S_{\mathrm{mn}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{g=1}{\overset{G}{\mathrm{\Σ}}}H({\mathrm{\ϵ}}_r-|r_{\mathrm{mk}}^i-r_{\mathrm{ng}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θx}}-|{\mathrm{\θ}}_{\mathrm{mkx}}^i-{\mathrm{\θ}}_{\mathrm{ngx}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θy}}-|{\mathrm{\θ}}_{\mathrm{mky}}^i-{\mathrm{\θ}}_{\mathrm{ngy}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θz}}-|{\mathrm{\θ}}_{\mathrm{mkz}}^i-{\mathrm{\θ}}_{\mathrm{ngz}}^{i+1}\left|\right)---\left(3\right)$

Wherein, H (r, θ _x, θ _y, θ _z) be step function:

$H(r,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)=\left\{\begin{array}{cc}1,& r>0,{\mathrm{\θ}}_x>0,{\mathrm{\θ}}_y>0\mathrm{and}{\mathrm{\θ}}_z>0;\\ 0,& \mathrm{otherwise}...\end{array}\right.,---\left(4\right)$

ε _rBe the threshold value in space utmost point footpath, value is less than 5 pixels usually.ε _{θ x}, ε _{θ y}And ε _{θ z}Be respectively the setting threshold of three direction of principal axis projection angles, value is less than 30 ° usually.For candidate's particle point that each m in the i+1 two field picture is ordered, can be according to objective function S _MnObtain a similarity coefficient, the point of similar value maximum wherein, being with particle center of mass point m to be matched is the match point of same particle.

Many bubble diagrams as example, Figure 4 shows that particle (bubble) sequence image that the three-dimension measuring system based on the separate unit high-speed camera absorbs as motion match in the biphase gas and liquid flow.Through a series of Digital Image Processing, comprise gray processing, poor shadow inverse, filtering, Threshold segmentation, morphology processing, image filling and connected component labeling and elimination, can extract the two-dimentional center-of-mass coordinate of each particle (bubble), according to existing parameter and mathematical model, calculate the three-dimensional center-of-mass coordinate of each particle (bubble), as matching characteristic.

Based on the particle three-dimensional matching process of volume coordinate, adjacent two frame particles (bubble) are carried out motion match in according to the present invention, can effectively reconstruct particle (bubble) 3 D motion trace based on sequence image on this basis.This inventive method is practical, can realize accurately and efficiently the three-dimensional motion coupling of particle picture in the polyphasic flow.

Claims (3)

1. particle three-dimensional motion match method based on space polar coordinate, it is characterized in that, comprise the following steps: utilizing the three-dimensional measurement platform to obtain on the basis of Double-visual angle particle original image, by Digital Image Processing, according to the particle provincial characteristics, extract the two-dimentional center-of-mass coordinate of each particle in the synchronization different visual angles, based on how much of polar curves and particle property constraint condition, determine the corresponding relation of same particle in different visual angles, simultaneously in conjunction with accurate on-site proving parameter and three-dimensional measurement model, calculate the three-dimensional center-of-mass coordinate of particle in the single-frame images, with the particle three-dimensional characteristic parameter as matching characteristic, set spherical query window, set up space polar coordinate system, ask for respectively the projection angle of coordinate system on three direction of principal axis, and in conjunction with the threshold value constraint of space utmost point footpath distance, thereby uniquely determine the spatial point that same particle moves in multiple image.

2. the particle three-dimensional motion match method based on space polar coordinate as claimed in claim 1 is characterized in that described step further is refined as:

1) the continuous multiple frames Double-visual angle particle picture to obtaining utilizes digital image processing techniques, extracts the two-dimentional center-of-mass coordinate of each particle, according to existing calibrating parameters and measurement model, calculates the three-dimensional center-of-mass coordinate of each particle;

2) in the first two field picture, point centered by particle barycenter to be matched is set spherical query region take the maximum range value of interframe Particles Moving as radius, and other particles in the zone are its neighbor point, set up space polar coordinate system take central point as initial point;

3) in the second two field picture, may with particle to be matched in the first frame be same particle be called candidate's particle, its barycenter is candidate point, centered by candidate point, offer equally the spherical query window identical with the first frame radius value, and set up corresponding space polar coordinate system, the neighbor point that other particle barycenter in the query region are candidate point;

4) respectively in the first frame and the second two field picture, calculate the space utmost point footpath distance value of each neighbor point and central point and the projection angle of three change in coordinate axis direction, and the calculated value apart from calculated value and three angles of each neighbor point in the first frame and the second frame compared, and setting threshold constraint;

5) definition similarity coefficient objective function, each candidate point in the second frame can draw a corresponding similarity coefficient, and satisfies the candidate point that threshold condition is at most the similarity coefficient maximum, and being with particle to be matched is the motion match point of same particle.

3. the particle three-dimensional motion match method based on space polar coordinate as claimed in claim 1 is characterized in that, the concrete steps of determining the spatial point that same particle moves in multiple image are:

The three-dimensional center of mass point of each particle is set spherical query window radius R in obtaining continuous two width of cloth images _hThreshold value is the largest motion distance, delta d that is not less than particle _Max, generally get R _h=Δ d _Max

Suppose that the two continuous frames image is respectively i frame and i+1 frame, then in the i two field picture, take particle three-dimensional center of mass point m to be matched as the centre of sphere, R _hFor radius is made a spherical query region, the volume coordinate of some m is

Except a m, also have K particle in this zone, be called the neighbor point of a m, with m _kExpression (k=1 ..., K), its volume coordinate is respectively

Take a m as initial point, set up space polar coordinate system, then the relation of other neighbor points and m can be by space utmost point footpath in the i two field picture

With three axial projection angles

Next unique definite, wherein

$r_{\mathrm{mk}}^i=\sqrt{{(x_{\mathrm{mk}}^i-x_m^i)}^2+{(y_{\mathrm{mk}}^i-y_m^i)}^2+{(z_{\mathrm{mk}}^i-z_m^i)}^2}---\left(1\right)$

${\mathrm{\θ}}_{\mathrm{mkx}}^i=\arcsin \frac{x_{\mathrm{mk}}^i-x_m^i}{r_{\mathrm{mk}}^i},$ ${\mathrm{\θ}}_{\mathrm{mky}}^i=\arcsin \frac{y_{\mathrm{mk}}^i-y_m^i}{r_{\mathrm{mk}}^i},$ ${\mathrm{\θ}}_{\mathrm{mkz}}^i=\arcsin \frac{z_{\mathrm{mk}}^i-z_m^i}{r_{\mathrm{mk}}^i}---\left(2\right)$

In the i+1 two field picture, may with particle to be matched in the i frame be same particle be referred to as candidate's particle, its center of mass point is candidate point, represents with n.For a n, offering equally the Radius value is R _hSpherical query window, and set up corresponding space polar coordinate, wherein n _g(g=1 ..., G) be the neighbor point of candidate point, G is the number of neighbor point, the space utmost point directly is Three axial projection angles are respectively

According to i frame and i+1 frame hollow compole footpath and projection angle value definition similarity coefficient function S _Mn:

$S_{\mathrm{mn}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{g=1}{\overset{G}{\mathrm{\Σ}}}H({\mathrm{\ϵ}}_r-|r_{\mathrm{mk}}^i-r_{\mathrm{ng}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θx}}-|{\mathrm{\θ}}_{\mathrm{mkx}}^i-{\mathrm{\θ}}_{\mathrm{ngx}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θy}}-|{\mathrm{\θ}}_{\mathrm{mky}}^i-{\mathrm{\θ}}_{\mathrm{ngy}}^{i+1}|,{\mathrm{\ϵ}}_{\mathrm{\θz}}-|{\mathrm{\θ}}_{\mathrm{mkz}}^i-{\mathrm{\θ}}_{\mathrm{ngz}}^{i+1}\left|\right)---\left(3\right)$

Wherein, H (r, θ _x, θ _y, θ _z) be step function:

$H(r,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)=\left\{\begin{array}{c}1,r>0,{\mathrm{\θ}}_x>0,{\mathrm{\θ}}_y>0\mathrm{and}{\mathrm{\θ}}_z>0;\\ 0,\mathrm{otherwise}...\end{array}\right.,---\left(4\right)$

ε _rBe the threshold value in space utmost point footpath, value is less than 5 pixels usually; ε _{θ x}, ε _{θ y}And ε _{θ z}Be respectively the setting threshold of three direction of principal axis projection angles, value is less than 30 ° usually; For candidate's particle point that each m in the i+1 two field picture is ordered, can be according to objective function S _MnObtain a similarity coefficient, the point of similar value maximum wherein, being with particle center of mass point m to be matched is the match point of same particle.

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