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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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/11—Region-based segmentation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/136—Segmentation; Edge detection involving thresholding
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/20—Analysis of motion
- G06T7/246—Analysis of motion using feature-based methods, e.g. the tracking of corners or segments
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/60—Analysis of geometric attributes
- G06T7/62—Analysis of geometric attributes of area, perimeter, diameter or volume
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10072—Tomographic images
- G06T2207/10081—Computed x-ray tomography [CT]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20024—Filtering details
- G06T2207/20032—Median filtering
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20112—Image segmentation details
- G06T2207/20152—Watershed segmentation
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 Geotechnical Engineering micro-assay field, more particularly, to a kind of based on spheric harmonic function invariant
Particle recognition and method for tracing.
Background technology
In recent years, as the further investigation of the complicated mechanical behavior to rock soil medium material, increasing scholar start
Focus on the microcosmic soil mechanics behavior of the soil body.In this context, ground advanced numerical analogue technique Discrete-parcel method and X- in situ
Miniature soil mechanics under ray high precision computation machine tomography (CT) scanning is tested to have obtained rapid development, with discrete element simulation soil
The loading procedure of body, easily it can identify and follow the trail of particle and obtain its motor behavior, displacement and the amount of spin of such as particle.
However, there is substantial amounts of simplification and supposed premise in method for numerical simulation, it is impossible to truly reflect the complicated category of rock soil medium material
Property.Therefore, tested using the miniature soil mechanics under X-ray high accuracy CT scan in situ to study the Micromechanics behavior of the soil body
Become the inexorable trend of Development of Soil Mechanics.However, it is different from discrete element simulation, in the miniature soil mechanics experiment under CT scan
One key technology is exactly to realize the identification and tracking of particle under different stress states, and then obtains the motor behavior of particle.
In order to solve sand in the earliest miniature triaxial test proposed under CT scan in 2012 such as this key technology, Ando
The identification of grain and method for tracing.Its basic ideas is to carry out careful comparison to the volume of sand grains under different stress states, is recognized
It is closest for volume of the same sand grains under different conditions, it should be noted, however, that arriving, for a sand sample, sand grains
Quantity it is often very huge, the volume of many sand grains is all very close, in addition, will also result in for the processing procedure of CT images
Some errors of sand-grain volume.Therefore, single to identify and follow the trail of sand grains on from volume ratio, its recognition result often exists very big
Error, based on this, Ando etc. is further proposed sample decomposition into some small search windows, and proposes the motion tool of sand grains
There is the supposed premise of harmony to improve the recognition efficiency of feed consumption and precision, however, this dividing method and supposed premise are not
By shearing in formed shear band suitable for sample, the soil mechanics experiment under the conditions of more unsuitable large deformation, as simple shear,
Ring shear test etc..
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, the invention provides a kind of based on spheric harmonic function invariant
Particle recognition and method for tracing, the humorous invariant of ball by introducing particle characterize the three-dimensional configuration feature of particle, then by right
The second order norm distance of the humorous invariant of ball of the particle under different conditions is compared to quantify the similitude between particle shape,
And then multiple dimensioned matching is carried out to particle, thus solve the identification accuracy of particle and the technical problem that applicability is low.
To achieve the above object, according to one aspect of the present invention, there is provided a kind of based on spheric harmonic function invariant
Grain identification and method for tracing, it is characterised in that this method comprises the following steps：
(a) choose a pile particle and be made as particle specimens, obtain the particle specimens of original state, change in the particle specimens
Relative position between particle, obtains the particle specimens of deformation state, the particle under the CT scan original state and deformation state
Sample, respective CT images view is obtained respectively；
(b) image procossing and analysis are carried out to the CT images view of the original state and deformation state respectively, obtains it
In each particle volume, surface area, three-dimensional dimension, center-of-mass coordinate and three-dimensional major axes orientation, meanwhile, pass through gray scale between particle
It is worth different respectively to each particle numbering in the CT images view of the original state and deformation state；
(c) boundary pixel of each particle in the CT images view of the original state and deformation state is detected respectively, and
Three-dimensional of each summit of composition particle surface in 3 d space coordinate system is obtained according to the rate conversion of differentiating of the boundary pixel
Coordinate, the three-dimensional coordinate is converted into by polar coordinates by Coordinate Conversion, is derived from the pole on all summits of the particle surface
Coordinate simultaneously forms polar coordinates collection, and the polar coordinates collection is approached using spheric harmonic function sequence so that each particle passes through a ball
Hamonic function characterizes its three-dimensional surface morphology, so that each in the CT images view of the original state and deformation state
Grain is respectively formed corresponding spheric harmonic function, while calculates spheric harmonic function invariant corresponding to the spheric harmonic function；
(d) the particle j in the CT images view of the deformation state is calculated one by one and the CT images of the original state regard
Spheric harmonic function invariant second order norm distance between each particle in figure, obtains the CT images view in the original state
In the particle minimum with the spheric harmonic function invariant second order norm of particle j distance, the particle of distance minimum is
To be identified particles of the particle j in the original state, while the numbering of the particle j is changed to distance minimum
The numbering of particle, when each particle in the CT images view of the deformation state completes the change of numbering, described in completion
The identification of each particle in the CT images view of deformation state, so as to realize the identification of particle, wherein, j=1,2 ..., N, N be
The total quantity of particle.
It is further preferred that in step (b), described image processing and analysis include：The original state is obtained first
With the binary image of particle in the CT images view of deformation state, three-dimensional median filter then is used to the binary image
Handled, finally all particles to contact with each other in filtered image are separated using three-dimensional watershed algorithm.
It is further preferred that in step (c), the spheric harmonic function preferably uses following expression formula,
Wherein,It is on zenith angle θ and azimuth under spherical coordinate systemSpheric harmonic function, θ ∈ [0, π],It is spherical harmonic coefficient corresponding to spheric harmonic function n-th order m level items,It is corresponding to spheric harmonic function n-th order m level items
Legnedre polynomial.
It is further preferred that in step (d), the spheric harmonic function invariant preferably uses following expression formula
Wherein,It is spheric harmonic functionInvariant,It is the second order of spheric harmonic function n-th order
Norm,It is spheric harmonic functionThe frequency content of n-th order.
It is further preferred that in step (d), the spheric harmonic function invariant second order norm distance preferably uses following table
Up to formula,
Wherein, SH (f) is spheric harmonic function invariant of the particle in original state, and SH (g) is ball of the particle in deformation state
Hamonic function invariant, | | fn| | it is second order norm of the particle in the spheric harmonic function n-th order of original state, | | gn| | it is that particle is becoming
The second order norm of the spheric harmonic function n-th order of shape state.
It is further preferred that characterized in that, in step (c), the maximum order of the spheric harmonic function is chosen for 15.
It is further preferred that characterized in that, after the particle recognition is completed, obtain respectively in the original state and
The barycenter and major axes orientation of particle under deformation state, the change of the barycenter and major axes orientation under the original state and deformation state
It is particle motor behavior to change, and is achieved in the tracking of particle motor behavior.
In general, by the contemplated above technical scheme of the present invention compared with prior art, it can obtain down and show
Beneficial effect：
1st, the present invention characterizes the three-dimensional configuration feature of particle by introducing the humorous invariant of ball of particle, then by particle
The second order norm distance of the humorous invariant of ball under different conditions is compared to quantify the similitude between particle shape, and then
Multiple dimensioned matching is carried out to particle, realizes in the experiment of the miniature soil mechanics under high-precision CT scan and identifies different stress states
Under sand grains, improve the accuracy and applicability of the recognition methods, its is applied to all kinds of miniature soil mechanics of large deformation condition
Experiment；
2nd, particle recognition provided by the invention and tracer technique, efficiently identify micro- under in situ X-ray diffraction high accuracy CT scan
The sand grains of different load phases in the experiment of type soil mechanics, and then the motor behavior of all sand grains is followed the trail of exactly, such as
Displacement and amount of spin etc., the soil mechanics experiment being particularly suitable under the conditions of large deformation, such as simple shear, ring shear test；
3rd, recognition methods provided by the invention, step is simple, strong applicability, can be accurate and quickly to after deformation
Grain is identified, after particle recognition success, then by calculating barycenter and major axes orientation can of the particle under different conditions
The motor behavior of particle is tracked exactly, is had wide range of applications.
Brief description of the drawings
Fig. 1 is the flow chart according to the particle recognition constructed by the preferred embodiment of the present invention and tracking；
Fig. 2 (a) is according to the selection sand grains schematic diagram constructed by the preferred embodiments of the present invention；
Fig. 2 (b) is the schematic diagram according to the preparation particle specimens constructed by the preferred embodiments of the present invention；
Fig. 2 (c) is according to the schematic diagram that particle specimens are placed on to scanning platform constructed by the preferred embodiments of the present invention；
Fig. 2 (d) is the X ray CT scanning process according to the particle specimens constructed by the preferred embodiments of the present invention；
Fig. 3 be according to the particle specimens constructed by the preferred embodiments of the present invention in an initial condition with deformation state
CT images view；
Fig. 4 (a) is according to the particle specimens CT images figure constructed by the preferred embodiments of the present invention；
Fig. 4 (b) is according to the image after the particle specimens CT images figure binaryzation constructed by the preferred embodiments of the present invention；
Fig. 4 (c) be according to constructed by the preferred embodiments of the present invention to the image after the three-dimensional median filter process of Fig. 4 (b)；
Fig. 4 (d) is that Fig. 4 (c) is separated using three-dimensional watershed algorithm according to constructed by the preferred embodiments of the present invention
Contact the image after particle；
Fig. 5 (a) is the CT sample influence figures according to the particle constructed by the preferred embodiments of the present invention；
Fig. 5 (b) is rebuild together according to the order frequency composition of use 15 superposition constructed by the preferred embodiments of the present invention
Particle shape；
Fig. 5 (c) is according to 0 rank spheric harmonic function constructed by the preferred embodiments of the present invention；
Fig. 5 (d) is the particle shape according to 2~4 spheric harmonic functions constructed by the preferred embodiments of the present invention；
Fig. 5 (e) is the particle shape according to 5~8 rank spheric harmonic functions constructed by the preferred embodiments of the present invention；
Fig. 5 (f) is the particle shape according to 9~15 rank spheric harmonic functions constructed by the preferred embodiments of the present invention；
Fig. 6 is to identify sand two according to the particle recognition technology using the present invention constructed by the preferred embodiments of the present invention
Particle under individual state；
Fig. 7 is to be followed the trail of according to some particle constructed by the preferred embodiments of the present invention from original state to deformation state
The displacement arrived and amount of spin.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below
Conflict can is not formed each other to be mutually combined.
Fig. 1 is the flow chart according to the particle recognition constructed by the preferred embodiment of the present invention and tracking, as shown in figure 1, pressing
According to a preferred embodiment of the present invention, the detailed implementation process of specific steps is as follows：
(1) CT scan of sand sample
X ray CT scan is carried out to the different conditions of sand sample, Fig. 2 (a) is according to the preferred embodiments of the present invention institute
The selection sand grains schematic diagram of structure, Fig. 2 (b) are according to the preparation particle specimens constructed by the preferred embodiments of the present invention
Schematic diagram, Fig. 2 (c) are according to the signal that particle specimens are placed on to scanning platform constructed by the preferred embodiments of the present invention
Figure, Fig. 2 (d) is the X ray CT scanning process according to the particle specimens constructed by the preferred embodiments of the present invention, as Fig. 2 (a)~
(d) shown in, first, sand grains is as research object between random selection a pile 1mm~2mm (shown in such as Fig. 2 (a))；Will be all
Sand grains, which loads in the polycarbonate plastic sleeve pipe that an internal diameter is Φ 10mm, a height of 12mm, carries out sample preparation, and is entered using silica gel oil
Row is fixed (shown in such as Fig. 2 (b))；The sand sample made is fixed on a rotation branch for being applied to CT system scanning platform
On frame (shown in such as Fig. 2 (c))；It is positioned over again and the CT scan of 360 degree is completed under the X-ray source of CT system, and at rear
Detector on complete CT imaging (such as Fig. 2 (d) shown in).By the CT scan of initial sample as reference state.Then, steel is used
Nail is stirred to the sand grains in sleeve pipe, large deformation state of the simulation sand under ring shear test, then completes the CT of 360 degree
Scanning and CT imagings.Fig. 3 be according to the particle specimens constructed by the preferred embodiments of the present invention in an initial condition with become shape
CT images view under state, as shown in Figure 3, it can be noted that all there occurs huge displacement and rotation for all sand grains.Therefore, need
To number, the particle of sample in a deformed state is identified, so as to realize it according to the particle of sample in an initial condition
The tracking of motor behavior.
(2) processing and analysis of CT images
Fig. 4 (a) is according to the particle specimens CT images figure constructed by the preferred embodiments of the present invention, and Fig. 4 (b) is according to this
The image after particle specimens CT images figure binaryzation constructed by the preferred embodiment of invention, Fig. 4 (c) are according to the excellent of the present invention
Select constructed by embodiment to the image after the three-dimensional median filter process of Fig. 4 (b), Fig. 4 (d) be according to the present invention be preferable to carry out
The image after particle is contacted using the separation of three-dimensional watershed algorithm to Fig. 4 (c) constructed by example, as shown in Fig. 4 (a), it is shown that
One original CT images, including four carbonic ester plastic bushing, silica gel oil, sand grains and air phases, the present invention mainly borrows
The image processing software ImageJ that helps increase income carries out image procossing, first, is handled using threshold values and filters acid esters plastic bushing
With silica gel oil phase, the binary image only containing sand grains phase is obtained, the gray value of its sand grains pixel is 256, background pixel
Gray value is 0, sees Fig. 4 (b)；Because CT images can have some noise pixels after binary conversion treatment, filtered using three-dimensional intermediate value
Ripple device is handled, and filtering strength is 5 pixels, sees Fig. 4 (c)；Finally, the particle using three-dimensional watershed algorithm to all contacts
Separated, and each particle is numbered using a series of continuous gray values, see Fig. 4 (d).
(3) the spheric harmonic function analysis of particle shape
Based on CT images after image procossing, for certain single sand grains, its pixel volume elements included can be compiled by its gray scale
Number quick identification.The boundary pixel of particle is detected using the boundary pixel searching algorithm in ImageJ, and is differentiated according to pixel
Rate conversion obtains the apex coordinate collection V (x, y, z) of one group of composition particle surface.The present invention converts to obtain sand grains using spherical coordinates
The polar coordinates collection of outline, then the three-dimensional surface morphology of sand grains is rebuild using three-dimensional spheric harmonic function sequence, its basic thought is
The polar coordinates collection of one unit ball is expanded into by the corresponding polar coordinates collection of actual sand grains by approaching for spheric harmonic function sequence, and
Corresponding spherical harmonic coefficient is tried to achieve, it is as follows：
In formula, θ ∈ [0, π] andZenith angle and the azimuth of spherical coordinate system are represented respectively.Wherein,It is
M base of n ranks of spheric harmonic function, determined by formula (2),It is its corresponding spherical harmonic coefficient.
In formula,For associated Legnedre polynomial.Wherein, n is one between 0 Dao just infinite integer, tool
Body value determines by the reconstruction accuracy of sand grains, one group of spherical harmonic coefficientSum be (n+1)2。
It is (n+1) that existing surface polar coordinates collection, which is substituted into, and can obtain a unknown number in formula (1)2Linear equation
Group, found that the three-dimensional of nature sand grains when maximum order uses 15, can be fitted well according to substantial amounts of spheric harmonic function analysis
Morphological feature, therefore, the spheric harmonic function maximum order n used in the present inventionmax, can be in the hope of using Least Square Method for 15
This group of spherical harmonic coefficient.Fundamental property based on spheric harmonic function, invention introduces one group of humorous invariant of ball, i.e. spheric harmonic function not
The energy of the frequency content of same order characterizes the Analysis On Multi-scale Features of particle shape, such as following formula 3.
In formula,RepresentIn the frequency content of not same order, can be expressed as：
Two norms can be calculated by equation below:
Fig. 5 (a) is the CT sample influence figures according to the particle constructed by the preferred embodiments of the present invention, Fig. 5 (b) be according to
The particle shape rebuild together of the order frequency composition of use 15 superposition constructed by the preferred embodiments of the present invention, Fig. 5 (c) be according to
0 rank spheric harmonic function constructed by the preferred embodiments of the present invention, Fig. 5 (d) are according to 2 constructed by the preferred embodiments of the present invention
The particle shape of~4 spheric harmonic functions, Fig. 5 (e) are according to 5~8 rank spheric harmonic functions constructed by the preferred embodiments of the present invention
Particle shape, Fig. 5 (f) are according to the particle shape of 9~15 rank spheric harmonic functions constructed by the preferred embodiments of the present invention, are such as schemed
Shown in 5 (a)~(f), it can be seen that the particle shape (Fig. 5 (b)) and its CT shadow rebuild together using the superposition of 15 order frequency compositions
Picture (Fig. 5 (a)) is basically identical, wherein, 0 order frequency composition represents the volume size (Fig. 5 (c)) of particle；2~4 order frequency compositions
Represent the general form (Fig. 5 (d)) of particle；5~8 ranks represent the local corner angle feature (Fig. 5 (e)) of particle；The representative of 9~15 ranks
The textural characteristics (Fig. 5 (f)) on grain surface.
(4) the Based on Multiscale Matching algorithm of particle shape
In order to evaluate the similitude between variable grain form, the present invention proposes that the Multiscale Morphological of global alignment particle is special
The method of sign, i.e., quantify the gap of its form according to the second order norm distance of the 15 humorous invariants of rank ball between particle, such as following formula institute
Show：
In formula, f and g represent the ball of some particle under the spheric harmonic function of some particle and deformation state under original state respectively
Hamonic function.
Pass through the detailed calculating to the second order norm distance of the humorous invariant of ball between particle under two states, it is believed that when two
Between particle the norm apart from it is minimum when, the two particles be same particle two states.Fig. 6 is according to the preferred of the present invention
The particle under particle recognition technology identification two states of sand using the present invention constructed by embodiment, as shown in fig. 6, its
In, identical color represents the same particle under two states.The accuracy of recognition result can be seen that very by range estimation
It is good.By further checking discovery, using the rate of accuracy reached of the inventive method particle recognition to 98%, and use traditional
Volume ratio only has 26% to the accuracy rate of recognition methods.Becoming greatly therefore, it can be said that bright traditional method is not particularly suited for sample
The particle recognition of shape, and invented party's rule is perfectly suitable for the particle recognition under sample large deformation.
After particle recognition success, calculate barycenter and major axes orientation can of the particle under different conditions and follow the trail of exactly
To the motor behavior of particle.Fig. 7 be according to the same particle constructed by the preferred embodiments of the present invention from original state to change
The displacement and amount of spin that shape state tracks, as shown in fig. 7, in figure the original state barycenter of particle in 3 d space coordinate and
Coordinate in spherical coordinate system is respectively (1.48mm, 1.33mm, 1.89mm), and (81 °, 131 °), barycenter in a deformed state exists
In 3 d space coordinate with the coordinate in spherical coordinate system respectively (1.56mm, 1.59mm, 1.72mm), (63 °, 155 °), therefore,
The displacement of particle motion is (0.08mm, 0.26mm, -0.17mm), and the corner of motion is (- 18 °, 24 °)
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, all any modification, equivalent and improvement made within the spirit and principles of the invention etc., all should be included
Within protection scope of the present invention.
Claims (7)
1. a kind of particle recognition and method for tracing based on spheric harmonic function invariant, it is characterised in that this method includes following step
Suddenly：
(a) choose a pile particle and be made as particle specimens, obtain the particle specimens of original state, change particle in the particle specimens
Between relative position, obtain the particle specimens of deformation state, the particle specimens under the CT scan original state and deformation state,
Respective CT images view is obtained respectively；
(b) image procossing and analysis are carried out to the CT images view of the original state and deformation state respectively, obtained wherein every
Volume, surface area, three-dimensional dimension, center-of-mass coordinate and the three-dimensional major axes orientation of individual particle, meanwhile, by gray value between particle not
With respectively to each particle numbering in the CT images view of the original state and deformation state；
(c) boundary pixel of each particle in the CT images view of the original state and deformation state is detected respectively, and according to
The rate conversion of differentiating of the boundary pixel obtains three-dimensional coordinate of each summit of composition particle surface in 3 d space coordinate system,
The three-dimensional coordinate is converted into by polar coordinates by Coordinate Conversion, is derived from the polar coordinates on all summits of the particle surface simultaneously
Polar coordinates collection is formed, the polar coordinates collection is approached using spheric harmonic function sequence so that each particle passes through a spheric harmonic function
To characterize its three-dimensional surface morphology, so that each equal shape of particle in the CT images view of the original state and deformation state
Into corresponding spheric harmonic function, while pass through spheric harmonic function invariant corresponding to spheric harmonic function acquisition；
(d) in the CT images view for calculating the particle j and the original state in the CT images view of the deformation state one by one
Each particle between spheric harmonic function invariant second order norm distance, obtain in the CT images view of the original state with
The particle of the spheric harmonic function invariant second order norm distance minimum of the particle j, the minimum particle of the distance is described
To be identified particles of the particle j in the original state, while the numbering of the particle j is changed to the minimum particle of the distance
Numbering, when each particle in the CT images view of the deformation state complete numbering change when, complete the deformation
The identification of each particle in the CT images view of state, so as to realize the identification of particle, wherein, j=1,2 ..., N, N be particle
Total quantity.
2. a kind of particle recognition and method for tracing based on spheric harmonic function invariant as claimed in claim 1, it is characterised in that
In step (b), described image processing and analysis include：The CT images view of the original state and deformation state is obtained first
The binary image of middle particle, then the binary image is handled using three-dimensional median filter, finally using three-dimensional
Watershed algorithm separates to all particles to contact with each other in filtered image.
3. a kind of particle recognition and method for tracing based on spheric harmonic function invariant as claimed in claim 1 or 2, its feature exist
In, in step (c), the spheric harmonic function preferably uses following expression formula,
Wherein,It is on zenith angle θ and azimuth under spherical coordinate systemSpheric harmonic function, θ ∈ [0, π], It is spherical harmonic coefficient corresponding to spheric harmonic function n-th order m level items,It is that Legendre corresponding to spheric harmonic function n-th order m level items is multinomial
Formula.
4. a kind of particle recognition and method for tracing based on spheric harmonic function invariant as described in claim any one of 1-3, its
It is characterised by, in step (d), the spheric harmonic function invariant preferably uses following expression formula
Wherein,It is spheric harmonic functionInvariant,It is the second order norm of spheric harmonic function n-th order,It is spheric harmonic functionThe frequency content of n-th order.
5. a kind of particle recognition and method for tracing based on spheric harmonic function invariant as described in claim any one of 1-4, its
It is characterised by, in step (d), the second order norm distance of the spheric harmonic function invariant preferably uses following expression formula,
<mrow>
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<mi>S</mi>
<mi>H</mi>
<mrow>
<mo>(</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
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<mi>H</mi>
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</mrow>
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</mrow>
<mi>&infin;</mi>
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Wherein, SH (f) is spheric harmonic function invariant of the particle in original state, and SH (g) is ball humorous letter of the particle in deformation state
Number invariant, | | fn| | it is second order norm of the particle in the spheric harmonic function n-th order of original state, | | gn| | it is that particle is becoming shape
The second order norm of the spheric harmonic function n-th order of state.
6. a kind of particle recognition and method for tracing based on spheric harmonic function invariant as described in claim any one of 1-5, its
It is characterised by, in step (c), the maximum order of the spheric harmonic function is 15.
7. a kind of particle recognition and method for tracing based on spheric harmonic function invariant as described in claim any one of 1-6, its
Be characterised by, after the particle recognition is completed, obtain respectively under the original state and deformation state the barycenter of particle and
Major axes orientation, the change of the barycenter and major axes orientation under the original state and deformation state are particle motor behavior, by
This realizes the tracking of particle motor behavior.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201710907157.6A CN107730513B (en) | 2017-09-29 | 2017-09-29 | A kind of particle recognition and method for tracing based on spheric harmonic function invariant |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
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