CN110598830A - Joint multi-cell tracking method based on label ant colony - Google Patents

Joint multi-cell tracking method based on label ant colony Download PDF

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CN110598830A
CN110598830A CN201910263691.7A CN201910263691A CN110598830A CN 110598830 A CN110598830 A CN 110598830A CN 201910263691 A CN201910263691 A CN 201910263691A CN 110598830 A CN110598830 A CN 110598830A
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徐本连
鲁明丽
陈庆兰
施健
孙乙丹
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Jiangsu Saikang Medical Equipment Co ltd
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Abstract

The invention discloses a label ant colony-based combined multi-cell tracking method. Firstly, generating a group of cell candidate ant colonies on a current frame by adopting a label-free scout ant colony, constructing a bipartite graph on the basis of the cell candidate ant colonies, and forming the bipartite graph by using the cell state estimated from the previous frame and the currently generated cell candidate ant colonies; secondly, optimally realizing interframe matching by using a label ant colony and taking track optimal mode distribution as a target function, wherein the multi-cell state is obtained by using the approximate multi-Bernoulli parameters of the evolved label ant colony, and the lineage tree of the cell is extracted by a track pheromone field on interframe matching determined by the lineage tree; finally, aiming at track fracture, a four-step track recovery method is provided so as to realize the association between the fractured tracks. The invention can extract the spectrum coefficient of the cell by using the trajectory pheromone, and estimate the state of the cell by using the food pheromone; compared with the prior art, the cell division precision and the recall rate are obviously improved.

Description

Joint multi-cell tracking method based on label ant colony
Technical Field
The invention belongs to the field of automatic tracking, and particularly relates to a label ant colony-based combined multi-cell tracking method.
Background
Quantitative analysis of cell behavior requires reliable automatic tracking techniques and the ability to automatically estimate the state, morphological parameters and corresponding lineage trees associated with each cell. The manual tracking has high requirements on the professional level of experimenters, and is time-consuming, difficult to copy results, difficult to track in parallel, easy to make mistakes and the like, so that the integrated automatic tracking technology is the main research focus in cell tracking in recent years.
At present, there are various methods for automatically tracking multiple cells, such as: a segmentation association method, a model evolution method and a filtering method. The segmentation correlation method is an effective path for solving the problem of low signal-to-noise ratio multi-cell division tracking, but the segmentation precision and the adopted data correlation method are critical to the tracking precision. The model tracking method can track the deformation of cells and automatically generate segmentation, and is easily influenced by the adjacent situations, such as cell overlapping, ant colony aggregation, adhesion and the like. The filtering method is generally classified into a Bayesian framework, such as a multi-hypothesis method, a particle filter, a combined probability data association algorithm and a random finite ant colony filtering method, and the most obvious characteristic of the methods is that the researches on cell division, newly entered cells, cell identity and other identification and estimation are not deep enough in the cell tracking field depending on a strict mathematical theory basis.
Data correlation has been a challenging problem in the field in the case of cell division, deformation and measurement uncertainty, closely related to which is the detection of segmentation and division events. The current segmentation methods mainly comprise a threshold method, a horizontal ant colony method, a graphic model method and some specially developed cell tracking software ant colony formers. Recently, machine learning methods such as convolutional neural networks have also been used for cellular complex image analysis. The cell division detection method mainly comprises a conditional random field method, a model evolution method and a model characteristic method, and meanwhile, a convolutional neural network is also used for detecting cell division, and the method can reach the expert cell labeling level. For cell tracking, algorithms such as integer programming, minimum cost flow and the like are commonly used as data association methods, but the performance of the algorithms depends on the accuracy of cell segmentation to a great extent, and data association and filtering algorithms are processed independently.
The invention provides a label ant colony-based multi-cell data association and state estimation joint tracking method. The invention firstly adopts a label-free scout ant colony to generate a group of cell candidate ant colonies on a current frame, a bipartite graph is constructed on the basis of the cell candidate ant colony, the bipartite graph is composed of a cell state estimated from a previous frame and a currently generated cell candidate ant colony, the matching between frames is optimally realized by utilizing the decision behavior of the label ant colony and distributing the label ant colony in a track optimal mode as a target function, finally, the multi-cell state is obtained by the approximate multi-Bernoulli parameters of the evolved label ant colony, and the lineage tree of the cell is extracted by a track pheromone field on the determined matching between frames. Aiming at track fracture, a four-step track recovery method is provided to realize the association between fractured tracks. The experimental result shows that the method provided by the invention can well track the difficult tracking problems of cell division, deformation, uncertainty of measurement and the like, and the tracking performance is greatly improved compared with the conventional multi-cell tracking method.
Ant colony: the ant colony formed by a plurality of ants is represented, wherein the decision-making behavior of each ant is random and simple, but the ant individuals cooperate with each other to jointly complete a certain complex task.
Labeling: cell tags are used to identify and uniquely identify cells by l ═ k1,i1) Is shown in which k is1Indicates the time at which the cell first appeared, i1Indicating the i-th occurrence at that moment1And (4) cells. When the cell is at time k2When splitting occurs, for labelling(j is 1, 2). For ease of reference in the figures, it will be generally usedIs marked as
Disclosure of Invention
1. The invention aims to provide a novel method.
The invention provides a combined tracking method of multi-cell data association and state estimation based on a label ant colony, aiming at solving the tracking problems of cell division, deformation, measurement uncertainty and the like. Firstly, a set of cell candidate ant colony is generated on the current frame by adopting a label-free scout ant colony, a bipartite graph is constructed on the basis of the cell candidate ant colony, the bipartite graph is composed of the cell state estimated on the previous frame and the cell candidate ant colony generated currently, the label ant colony is distributed as an objective function in a track optimal secondary mode to optimally realize matching between frames, finally, the multi-cell state is obtained by the approximate multi-Bernoulli parameters of the evolved label ant colony, and the cell lineage tree is extracted by a track pheromone field on the determined inter-frame matching. Finally, aiming at track fracture, a four-step track recovery method is provided to realize the correlation between fractured tracks.
2. The technical scheme adopted by the invention is disclosed.
The invention discloses a label ant colony-based combined multi-cell tracking method, which comprises the following steps:
multi-bernoulli random finite set definition and its approximation:
a finite set of multi-bernoulli randoms: the multi-Bernoulli random finite set X is a single Bernoulli random finite set X consisting of a set of a fixed number M(ζ)(1.. said., M) and each single bernoulli random finite set X(ζ)Can use its existence probability r(ζ)E (0,1) and its corresponding probability density function pi(ζ)To indicate that, then, a multi-bernoulli random finite set X can be used with a bernoulli parameter setTo represent; label multi-Bernoulli random finite set available { (r)(ζ),π(ζ)) ζ ∈ Ψ } represents, where Ψ represents a set of indices, to which a label is assigned if a single bernoulli component returns a non-empty set;
label multi-BernoulliAnd (3) utilizing random finite set approximation: the finite set of tags, i.e. the population of tagged Bernoulli ants, can be approximated byTherein, ΨaA set of ant colony indices is represented,representing a tagged ant colonyThe probability of the existence of (a) is,indicating label ant colonyA discrete probability density distribution ofIf the value is greater than a certain threshold value, the ant colony is considered to survive and is connected with a cell labelAre associated with whereinDefining an identity mapping from the ant colony index set to the cell signature; given a tag ant colonyProbability of its existenceCan be calculated as
Where s is an area integral variable, g(s) is a heuristic likelihood function, τ(ζ)Is a labelAnt colonyCorresponding pheromone field, R(ζ)As a tag ant colonyThe area of influence of (a);
cell frame-to-frame matching problem definition:
representing the estimated m cell locations at the k-th frame,representing the n cell candidate sets obtained at frame k +1, a bipartite graph G ═ (U, V, E) was constructed in which, e denotes the set of edge matching hypotheses from U to V, and the problem of inter-frame matching translates to
And isWherein D is(C)(. cndot.) represents a cost function for the premise of matching hypothesis C, f (-) represents the mapping of matching hypotheses from U to V, f-1(. h) represents the inverse mapping of f, |, represents the potential of some set;
the cost function D uses the optimal path sub-pattern assignment (OSPA-T), i.e.: given two sets of labeled sets X and Y, the number of elements is m and n, respectively, (X { (X)1,l1),...,(xm,lm) Denotes the set of estimated labeled l cell states x of the previous frame，Y＝{(y1,s1),...,(yn,sn) Denotes the subset of candidate metrics y corresponding to the current frame that match the hypothesis with the label s, OSPA-T is defined as OSPA-T if m ≦ n
Wherein d isc((x, l), (y, s)) -min (c, d ((x, l), (y, s))) represents the intercept distance, the parameters c and p represent the positive sensitivity coefficient (both greater than zero) for the difference in the number of elements of the two sets and the difference in the tagged state variables, respectively, ψnRepresenting a set of feasible perturbations on set Y,. psi (i) representing psinOf (a), a base distance d ((x, l), (y, s)) ═ d (x, y)p′+d(l,s)p′)1/p′P 'represents a base distance order parameter, d (x, y) represents a p' norm distance between two states x, y, d (l, s) represents a label error, d (l, s) equals 0 if l equals s, otherwise d (l, s) equals λ, λ ∈ [0, c ]](ii) a If m > n, there is Dp,c(X,Y)＝Dp,c(Y,X)；
Candidate set generation based on label-free scout ant colony
In the (k + 1) th frame, a given scout ant colony is initially randomly distributed in the current image area, a new ant dynamics system is introduced for modeling the behavior of the scout ant, namely, the scout ant dynamics system gradually evolves from chaotic behavior to deterministic behavior, so that the possible area of the food source is found; the kinetic behavior of a scout ant is defined as follows
Wherein the content of the first and second substances,represents the chaos movement variable of the scout ant during the t iteration, haExpressing the ant self-organizing factor, the value range is between 0 and 1,representing the status of the scout ant at the t-th iteration, parameter ψdParameter V representing the search range of ants in the search spaceaRepresenting different regions of the control search space, a, b being constants, pa(t-1) represents the optimal solution obtained by the scout ant and the neighbor ants thereof in the previous t-1 iterations;
representing scout antSet of neighboring ants at the t-th iteration, assuming scout antsAnd the current state and the optimal state of the former t-1 iterations of the neighboring ants are known, then the ant is detectedThe optimal state obtained in the previous t iterations is
Wherein, the symbol V represents the large operation, g-1(. represents an inversion operation on a likelihood function g defined as
Wherein, IlRepresenting intensity values, B, of the normalized gray-scale image at pixel lqRepresenting a set of pixels, N, comprised by a square region centred on a pixel q(q)Expressing a neighboring pixel set of a pixel q, wherein a symbol | · | expresses the number of elements in the set, and a symbol ^ expresses a small calculation; on the t-th iteration, if ant is detectedAt pixel q, then
Regarding ant states of the ant colony set in two successive iterations as a two-state setAndthen the OSPA-T is reduced to an optimal sub-modal allocation (OSPA) distanceThus, when ma≤naWhen there is
If ma＞naDefinition of
Step 1: initialization: given a plurality of groups of scout ant colonies, scout the chaos movement variable y in the dynamics behavior of the anta(0) Self-organizing factor haReconnaissance of initial state of antSearch scope parameter psidDifferent region parameters V of the search spaceaConstants a, b, etc. are known;
step 2: for each group of scout ant colony, each scout ant moves according to the dynamic behavior model, the likelihood function value of the corresponding pixel where the scout ant is located is sensed according to the likelihood function definition, and information exchange is carried out between the likelihood function value and the adjacent scout ant to obtain the optimal state obtained by the current iteration;
and step 3: if the pixel position of the detective ant is the position area where the possible cell is detected, setting the corresponding likelihood function as a very small value;
and 4, step 4: calculating the optimal sub-mode distribution distance between the current iteration scouting ant colony state set and the last iteration scouting ant colony state setIf the difference is smaller than a certain threshold value, the scouting work of the scout ant colony is terminated, and then a plurality of scout ant colonies are generated through cluster reconstruction;
and 5: repeating the steps 2-4 until no new reconnaissance ant colony is generated; the center of each generated scout ant colony is used as the centerThus, n candidate measurements are formed
Further, the specific method for matching construction and parameter estimation joint tracking based on the label ant colony is as follows:
set label multi-Bernoulli random finite set parameter { (r)(ζ),π(ζ)) ζ epsilon Ψ and label multi-bernoulli ant group parameter setThere is a one-to-one correspondence, and the tag colony of Bernoulli ants has a one-to-one correspondence with the cell, i.e.
Assuming that the tag is a ζ ant colony, the tag will move from the position of the previous frame to the position of the next frame with a survival probability, which is defined as:
where H, W denote the height and width of the current frame image,indicating the shortest height and width direction distance from the center of the tag ant colony to the image boundary at the k-th frame,representing the existence probability of the tag ant colony in the k frame;
similarly, the probability of the tag ant colony splitting at the next frame k +1 is defined as
Wherein exp (. cndot.) represents an exponential function,respectively represent cellsThe resulting contour aspect ratio is estimated at the k-th frame and the initial frame,respectively represent cellsAt the average intensity of the k-th and initial frames,υ is a regulation factor between 0 and 1,indicates the corresponding cellThe size of the local window area of (a),represents the estimated cells at the k frameThe area size;
based on the above definition, the tag ant colony-based interframe matching and parameter estimation integrated method is described as follows:
step 1: initialization: assuming there were m cell estimates in the previous frame k For the estimated location of cell i, its corresponding set of tagged Bernoulli ant population parameters can be expressed asFor each Bernoulli colony, the colony scales are allGeneration of n candidate measurement sets from unlabeled scout ant colonies Representing candidate metrology j locations;
step 2: bernoulli ant colony for any labelOptionally one of the labeled ants (corresponding to the label of the ant colony) randomly generating two random numbers kappaSE (0,1) and kME (0,1), if:
(1)：the tag ant can survive from the previous frame and estimate the position from the corresponding cellStarting with, selecting candidate metricsHas a probability of
Wherein 1 isY(X) denotes an inclusion function, ifThen equals 1, otherwise 0;is shown asA subset of candidate measurements corresponding to the estimated location of each cell,is shown in the trackThe intensity of the trace pheromone, theta (·) represents the identity function of the trace pheromone, which is associated with the cellCorrelation;representing an initiating function, and havingd (,) represents a distance function, α1,β1Representing a relative importance coefficient;
(2)：the ant can survive from the last frame and should have the possibility of cell division, so the tag ant is duplicated into two identical tag ants, and the positions of the two identical tag ants are estimated from the corresponding cellsStarting with, selecting different candidate measurementsHas a probability of
(3)：OrThe ant is still, which indicates that the corresponding cell may disappear in the next frame;
when the label ant decides according to (1) or (2), the passing track is followedUpper release of a certain amount of pheromone:
where p represents the pheromone residual coefficient,indicating that the current frame is k +1 corresponding label Bernoulli ant colonyLast iteration updateThe probability of presence obtained later on is,representing cellsThe area of influence of (a);
and step 3: after the m label Bernoulli ant colonies complete corresponding decisions according to the step 2, forming a matching hypothesis C from U to V, and calculating corresponding OSPA-T values;
and 4, step 4: according to the step 2-3, carrying outIs circulated secondarily inIn the secondary loop, the best matching hypothesis C of the iteration is obtained, and the corresponding candidate set is expressed asTo renThe labeled Bernoulli ant colony obtained according to step 2Starting cell state estimation, i.e. foraging; if a foraging ant is on pixel p, the probability that it moves to pixel q is defined as
Wherein alpha is2,β2Representing the relative importance coefficient, N(p)Representing a set of neighboring pixels of the pixel p,representing the intensity of the food pheromone at k +1 pixels q of the current frame; following the above decision, the targetThe swabs release a certain amount of pheromones on the pixel q simultaneously
Wherein epsilon1Is a threshold coefficient;
when labeled Bernoulli ant colonyAfter all ants finish the foraging decision, the corresponding food pheromone field is updated
Wherein the content of the first and second substances,representing the total information pixel input over pixel q,represents the total pixel spread input over pixel q, defined as
Wherein D represents a diffusion constant coefficient, the value range is (0,1), kappa is a control constant coefficient,representing pixels q anddistance between, RqRepresenting the area of influence of pixel q;
obtaining the label Bernoulli ant colony by using the obtained food pheromone field and a heuristic function after multiple iterationsBernoulli parameter ofApproximation
Wherein the content of the first and second substances,representing the probability density dispersion distribution of the foraging label ant colony of the current frame k +1,representing antsState of (1)The weight corresponding to the weight of the corresponding weight,representing a signature Bernoulli ant colonyThe number of ants in (1); for the food pheromone field, three simple processes of binarization, morphology and filling are carried out, and the contour and the position of the corresponding cell of the candidate set can be obtained
And 5: for the best matching hypothesis C obtained by the current iteration, the corresponding candidate set position, the track pheromone field and the food pheromone field are subjected to global updating
Wherein Q is1，Q2In order to enhance the constant for the pheromone,representing a candidate set obtained by the current iteration after the position corresponding to the optimal matching hypothesis C is updated;
step 6: repeating the steps 2-5 until the convergence condition is met; simultaneously, performing three-step simple processing of binarization, morphology and filling on the obtained food pheromone field obtained by the optimal matching iteration, and obtaining the labeled ant colonyProbability of existenceThe contour and position estimation of the corresponding cell can be obtained;
extracting a track pheromone field of the obtained optimal matching between frames, keeping the identity characteristics of the track pheromone, and forming a cell lineage tree through frame-frame sequential matching;
regarding unmatched candidate measurement as a new item which may appear in the current frame, correspondingly generating mutually independent tag Bernoulli ant colony, constructing a corresponding food pheromone field according to the step 4, and if the existing probability of the new tag ant colony is not lower than 0.5, extracting the outline and position estimation of the corresponding cell;
the positions obtained by the multiple label Bernoulli ant colonies are estimated to be close and the mutual distance is smaller than a certain threshold value, the label Bernoulli ant colony with high existence probability is reserved, and other label Bernoulli ant colonies meeting the conditions are directly removed and are not considered any more; meanwhile, for updating the label, the label which is the first to appear is given to the label Bernoulli ant colony with high existence probability.
Furthermore, the specific method for track recovery based on four stages is as follows:
the similarity standard for the four-stage based track recovery is as follows:
similarity standard 1: chi shape+，χ-Respectively representing the cell states of the flight path chi corresponding to the birth and ending moments, and for the two flight paths chi1Hexix-2If, ifThe ending time precedesThe similarity criterion 1 is defined as
Wherein R is-Represents a set of tracks satisfying the constraint condition of maximum moving distance between frames, and any track x thereof-The ending time precedes Representing corresponding track χ1The area of the cells at the time of birth is estimated,representing corresponding track χ2Estimating the area of the cell at the end moment, wherein n represents the intersection of the areas of the two cells, and U represents the sum of the areas of the two cells;
similarity criterion 2: for track χiThe state of the cell corresponding to the birth time k isFor trackThe cell states at times k and k-1 are respectivelyAndthe similarity criterion 2 is defined as
Wherein, Ch(. and C)w(. h) represents the lengths of the major and minor axes of the cell contour, respectively, Δ Ch(. phi.) and Δ Cw(-) represents the absolute value of the difference in length of the major and minor axes of the cell contour, respectively, and Δ A (·) represents the absolute value of the difference in cell area;
the method comprises the following specific steps:
stage 1: giving a time window with the length of 3 sampling intervals, sliding reversely from the last frame when the right side of the time window is at the starting position of the trackWhen intersecting, if the corresponding frame is the k-th frame, the intersecting track is associated with other tracks ending in the time window (from the k-3 th frame to the k-1 th frame); if the k-1 frame has a corresponding track candidate (namely the track is finished at the k-1 frame) and the constraint condition of the maximum moving distance between the frames is met, selecting the maximum one to be associated with according to the similarity standard 1; otherwise, entering stage 2;
and (2) stage: excluding phase 1 correlatedIf it isIf the space is not null and the frame k-2, k-3 has a corresponding track candidate (namely the track is ended in the frame k-2, k-3) and the constraint condition of the maximum moving distance between frames is met, the phase is determined according to the phaseSimilarity criterion 1 selects the largest one to associate with;
and (3) stage: excluding stages 1,2 already associatedIf it isComplete track of non-empty and adjacent (meeting the constraint of maximum moving distance between frames)Similarity standard 2 calculation is carried out on the k, k-1 frame, if the similarity value is larger than a given threshold value, the flight path x is calculatediIncorporated into flight pathCorresponding cell division;
and (4) stage: excluding stages 1,2, 3 already associatedIf it isIf the initial track is not empty, the initial track (and the track life is at least 3 sampling intervals) is considered as a formal track, otherwise, the track is removed.
3. The technical effect produced by the invention.
(1) The invention provides a combined tracking method of multi-cell data association and state estimation based on a label ant colony, wherein the data association and the state estimation are carried out in parallel and interactively; the method solves the problem of matching construction based on the label ant colony, is different from the common 1-1 matching, can process redundant candidate ant colony measurement, and continuously updates the candidate ant colony measurement position corresponding to the optimal matching through the foraging behavior of the ant colony, namely the matched candidate ant colony measurement is dynamically changed.
(2) The invention provides a new matching objective function, namely OSPA-T, which comprehensively considers potential, position and label matching errors.
(3) The invention can extract the spectrum coefficient of the cell by using the trajectory pheromone, and estimate the state of the cell by using the food pheromone; compared with the prior art, the cell division precision and the recall rate are obviously improved.
Drawings
FIG. 1 shows a sequence of multiple cell tracking (first row sequence 1, second row sequence 2).
FIG. 2 shows the sequence 1 tracking results (cell lineage tree), (a) three-dimensional lineage tree view 1, (b) three-dimensional lineage tree view 2, (c) three-dimensional lineage tree view 3, and (d) three-dimensional lineage tree view 4.
FIG. 3 is the sequence 2 trace results (cell lineage tree), (a) three-dimensional lineage tree view 1, (b) three-dimensional lineage tree view 2, (c) three-dimensional lineage tree view 3, and (d) three-dimensional lineage tree view 4.
Detailed Description
Example 1
1. Multi-bernoulli random finite ant colony definition and its approximation:
multi-bernoulli random finite ant colony: the multi-Bernoulli random finite ant colony X is composed of a group of a fixed number (such as M) of single-Bernoulli random finite ant colonies X(ζ)(1.... M.) and each single bernoulli random finite ant colony X(ζ)Can use its existence probability r(ζ)E (0,1) and its corresponding probability density function pi(ζ)To show that, the multiple Bernoulli random finite ant colony X can be a Bernoulli parameter ant colonyTo indicate. Tag multi-bernoulli random finite ant colony available { (r)(ζ),π(ζ)) ζ ∈ Ψ } representation, where Ψ represents an indexed ant colony, and a label is assigned to a single bernoulli component if it returns a non-empty ant colony.
Label multi-bernoulli random finite ant colony approximation: the tagged Bernoulli random finite ant colony can be approximated by a tagged Bernoulli ant colony, i.e.Wherein，ΨaIndicating the ant colony index ant colony combination,indicating label ant colonyThe probability of the existence of (a) is,indicating label ant colonyA discrete probability density distribution ofIf the value is larger than a certain threshold value, the ant colony is considered to survive and is connected with a cell labelAre associated with whereinDefined as the identity mapping from the ant colony index ant colony to cell signature. Given a tag ant colonyProbability of its existenceCan be calculated as
Where s is an area integral variable, g(s) is a heuristic likelihood function, τ(ζ)As a tag ant colonyCorresponding pheromone field, R(ζ)As a tag ant colonyThe area of influence of (c).
2. Cell frame matching problem definition
Representing the estimated m cell locations at the k-th frame,representing the n cell ant colony candidates obtained at frame k +1, a bipartite graph G ═ (U, V, E) was constructed in which, e denotes the ant colony from U to the edge on V (matching hypothesis), and the problem of inter-frame matching translates toAnd is Wherein D is(C)(. cndot.) represents a cost function for the premise of matching hypothesis C, f (-) represents the mapping of matching hypotheses from U to V, f-1(. h) represents the inverse mapping of f, |, represents the potential of some ant colony.
The cost function D uses the optimal path sub-pattern assignment (OSPA-T), i.e.: given two sets of labeled ant colonies X and Y, the number of elements is m and n, respectively, (X { (X)1,l1),...,(xm,lm) Denotes the ant colony of the cell states x with the label estimated in the previous frame, Y { (Y)1,s1),...,(yn,sn) Represents the sub ant colony of the candidate measurement y with the label s corresponding to the current frame, if m is less than or equal to n, OSPA-T is defined as
Wherein d isc((x, l), (y, s)) -min (c, d ((x, l), (y, s))) represents the intercept distance, and the parameters c and p represent the positive sensitivity coefficient (both greater than zero) for differences in the number of two ant colony elements and in the tagged state variable, respectively, ψnShowing feasibility perturbation of ant colony in ant colony Y,. psi (i) denotes psinOf (a), a base distance d ((x, l), (y, s)) ═ d (x, y)p′+d(l,s)p′)1/p′P 'represents a base distance order parameter, d (x, y) represents a p' norm distance between two states x, y, d (l, s) represents a label error, d (l, s) equals 0 if l equals s, otherwise d (l, s) equals λ, λ ∈ [0, c ]]. If m > n, there is Dp,c(X,Y)＝Dp,c(Y,X)。
3. Generation of candidate ant colony based on label-free scout ant colony
In the (k + 1) th frame, a given scout ant colony is initially randomly distributed in the current image area, and a new ant dynamics system is introduced for modeling the behavior of the scout ants, namely, the scout ant dynamics system gradually evolves from chaotic behavior to deterministic behavior, so that the possible area of the food source (cell) is found. The kinetic behavior of a scout ant is defined as follows
Wherein the content of the first and second substances,represents the chaos movement variable of the scout ant during the t iteration, haExpressing ant self-organizing factor, the value range is 0 and1 of the raw materials are added into the reactor,representing the status of the scout ant at the t-th iteration, parameter ψdParameter V representing the search range of ants in the search spaceaRepresenting different regions of the control search space, a, b being constants, pa(t-1) represents the optimal solution obtained by the scout ant and the neighbor ants in the previous t-1 iterations.
Representing scout antClose ant colony at the t-th iteration, assuming scout antAnd the current state and the optimal state of the former t-1 iterations of the neighboring ants are known, then the ant is detectedThe optimal state obtained in the previous t iterations is
Wherein, the symbol V represents the large operation, g-1(. represents an inversion operation on a likelihood function g defined as
Wherein, IlRepresenting intensity values, B, of the normalized gray-scale image at pixel lqRepresenting a group of ant pixels, N, included in a square region centered on a pixel q(q)The ant colony of the neighboring pixels of the pixel q is represented, the symbol | · | represents the number of elements in the ant colony, and the symbol ^ represents the minimization operation. At the t-th iterationGo up, if reconnaissance antAt pixel q, then
Regarding the ant state of the ant colony in two successive iterations as two-state ant colonyAndthen the OSPA-T is reduced to an optimal sub-modal allocation (OSPA) distanceThus, when ma≤naWhen there is
If ma＞naDefinition of
Based on the above definition, for the k +1 th frame cell image, the generation method of the multi-bernoulli random finite scout ant colony is as follows:
step 1: initialization: given a plurality of groups of scout ant colonies, scout the chaos movement variable y in the dynamics behavior of the anta(0) Self-organizing factor haReconnaissance of initial state of antSearch scope parameter psidDifferent region parameters V of the search spaceaThe constants a, b, etc. are known.
Step 2: for each group of scout ant colony, each scout ant moves according to the dynamic behavior model, the likelihood function value of the corresponding pixel where the scout ant is located is sensed according to the likelihood function definition, and information exchange is carried out between the likelihood function value and the adjacent scout ant to obtain the optimal state obtained by the current iteration.
And step 3: if the pixel position of the detective ant is the position area of the detected possible cell, the corresponding likelihood function is set to a small value.
And 4, step 4: calculating the optimal sub-mode distribution distance of the ant colony state ant colony of the iteration scout and the ant colony state ant colony of the last iteration scoutIf the difference is smaller than a certain threshold value, the scouting work of the scout ant colony is terminated, and then a plurality of scout ant colonies are generated through clustering reconstruction.
And 5: repeating steps 2-4 until no new scout ant colony is generated. The center of each generated scout ant colony is used as the centerThus, n candidate measurements are formed
4. Matching construction and parameter estimation joint tracking based on label ant colony
The invention relates to a label multi-Bernoulli random finite ant colony parameter ant colony { (r)(ζ),π(ζ)) Zeta ∈ Ψ } and label polynebieria parameter ant colonyThere is a one-to-one correspondence, and the tag bernoulli ant colony has a one-to-one correspondence with the cell, i.e.
Assuming that the tag is a ζ ant colony, the tag will move from the position of the previous frame to the position of the next frame with a survival probability, which is defined as:
where H, W denote the height and width of the current frame image,indicating the shortest height and width direction distance from the center of the tag ant colony to the image boundary at the k-th frame,indicating the probability of the existence of the tag ant colony at the k-th frame.
Similarly, the probability of the tag ant colony splitting at the next frame k +1 is defined as
Wherein exp (. cndot.) represents an exponential function,respectively represent cellsThe resulting contour aspect ratio is estimated at the k-th frame and the initial frame,respectively represent cellsAt the average intensity of the k-th and initial frames,υ is a regulation factor between 0 and 1,indicates the corresponding cellThe size of the local window area of (a),represents the estimated cells at the k frameThe size of the area.
Based on the above definition, the tag ant colony-based interframe matching and parameter estimation integrated method is described as follows:
step 1: initialization: assuming there were m cell estimates in the previous frame k For the estimated location of cell i, its corresponding tagged multi-bernoulli ant colony parameter ant colony can be expressed asFor each Bernoulli colony, the colony scales are allGeneration of n candidate measurement ant colonies from unlabeled scout ant colonies Representing candidate metrology j locations.
Step 2: bernoulli ant colony for any labelOptionally one of the labeled ants (corresponding to the label of the ant colony) randomly generating two random numbers kappaSE (0,1) and kME (0,1), if:
(1)：the tag ant can survive from the previous frame and estimate the position from the corresponding cellStarting with, selecting candidate metricsHas a probability of
Wherein 1 isY(X) denotes an inclusion function, ifThen equals 1, otherwise 0;is shown asCandidate measuring ant colonies corresponding to the estimated positions of the individual cells,is shown in the trackThe intensity of the trace pheromone, theta (·) represents the identity function of the trace pheromone, which interacts with the cellCorrelation;represents a heuristic function and hasd (,) represents a distance function, α1,β1The relative importance coefficients are expressed.
(2)：The ant can survive from the last frame and should have the possibility of cell division, so the tag ant is duplicated into two identical tag ants, and the positions of the two identical tag ants are estimated from the corresponding cellsStarting with, selecting different candidate measurementsHas a probability of
(3)：OrThe ant was immobilized, indicating that the corresponding cell may disappear in the next frame.
When the label ant decides according to (1) or (2), the passing track is followedUpper release of a certain amount of pheromone:
where p represents the pheromone residual coefficient,indicates that the current frame is k +1 corresponding to the labelBernoulli ant colonyThe resulting probability of presence after the last iteration update,representing cellsThe area of influence of (c).
And step 3: and (3) when the m label Bernoulli ant groups complete corresponding decisions according to the step 2, forming a matching hypothesis C from U to V, and calculating corresponding OSPA-T values.
And 4, step 4: according to the step 2-3, carrying outIs circulated secondarily inIn the secondary loop, the best matching hypothesis C of the iteration is obtained, and the corresponding candidate ant colony is expressed asTo renThe labeled Bernoulli ant colony obtained according to step 2Cell state estimation, i.e. foraging, is started. If a Formica foraging ant is on pixel p, its probability of moving to pixel q is defined as
Wherein alpha is2,β2Representing the relative importance coefficient, N(p)Representing a population of nearest neighbors to the pixel p,representing the intensity of the food pheromone at the current frame k +1 pixel q. Following the above decision, the tag ant releases a certain amount of pheromone on pixel q at the same time
Wherein epsilon1Is a threshold coefficient.
When labeled Bernoulli ant colonyAfter all ants finish the foraging decision, the corresponding food pheromone field is updated
Wherein the content of the first and second substances,representing the total information pixel input over pixel q,represents the total pixel spread input over pixel q, defined as
Wherein D represents a diffusion constant coefficient, the value range is (0,1), kappa is a control constant coefficient,representing pixels q anddistance between, RqRepresenting the area of influence of pixel q.
Using food obtained after a number of iterationsObtaining label Bernoulli ant colony by pheromone field and heuristic functionBernoulli parameter ofApproximation
Wherein the content of the first and second substances,representing the probability density dispersion distribution of the foraging label ant colony of the current frame k +1,representing antsState of (1)The weight corresponding to the weight of the corresponding weight,representing a signature Bernoulli ant colonyThe number of ants in (1). For the food pheromone field, three simple processes of binarization, morphology and filling are carried out to obtain the contour and position of the cells corresponding to the candidate ant colony
And 5: for the best matching hypothesis C obtained by the current iteration, the corresponding candidate ant colony positions, the track pheromone fields and the food pheromone fields are globally updated
Wherein Q is1，Q2In order to enhance the constant for the pheromone,and representing the candidate ant colony set obtained by the current iteration after the position corresponding to the optimal matching hypothesis C is updated.
Step 6: and (5) repeating the steps 2-5 until the convergence condition is met. Simultaneously, performing three-step simple processing of binarization, morphology and filling on the obtained food pheromone field obtained by the optimal matching iteration, and obtaining the labeled ant colonyProbability of existenceThe contour of the corresponding cell and its position estimate can be obtained.
And extracting the track pheromone field of the obtained best match between frames, retaining the identity characteristics of the track pheromone, and forming a cell lineage tree through frame-frame sequential matching.
And for unmatched candidate measurement, regarding the candidate measurement as a new item which may appear in the current frame, correspondingly generating mutually independent tag Bernoulli sub-ant colonies, constructing a corresponding food pheromone field according to the step 4, and if the existing probability of the new tag sub-ant colony is not lower than 0.5, extracting the outline and the position estimation of the corresponding cell.
And (3) for the position estimation neighbors obtained by the plurality of label Bernoulli ant colonies, if the mutual distance is less than a certain threshold value, the label Bernoulli ant colony with high existence probability is reserved, and other label Bernoulli ant colonies meeting the condition are directly removed without consideration. Meanwhile, for updating the label, the label which is the first to appear is given to the label Bernoulli ant colony with high existence probability.
5. Track recovery based on four steps
Aiming at the flight path generated by the method, the breakage phenomenon of the flight path can occur, and therefore, a reverse sliding time window flight path recovery four-step method is provided. The adopted association standard, except for satisfying the constraint condition of the maximum moving distance between frames, defines the following similarity standard:
similarity standard 1: chi shape+，χ-Respectively representing the cell states of the flight path chi corresponding to the birth and ending moments, and for the two flight paths chi1Hexix-2If, ifThe ending time precedesThe similarity criterion 1 is defined as
Wherein R is-Representing the flight path ant colony meeting the constraint condition of the maximum moving distance between frames, and any flight path x thereof-The ending time precedes Representing corresponding track χ1The area of the cells at the time of birth is estimated,representing corresponding track χ2The area of the cells at the end time is estimated, n represents the two-cell area ant population, and u represents the sum of the two-cell areas.
Similarity criterion 2: for track χiThe state of the cell corresponding to the birth time k isFor trackThe cell states at times k and k-1 are respectivelyAndthe similarity criterion 2 is defined as
Wherein, Ch(. and C)w(. h) represents the lengths of the major and minor axes of the cell contour, respectively, Δ Ch(. phi.) and Δ Cw(-) represents the absolute difference in length between the major and minor axes of the cell contour, respectively, and Δ A (·) represents the absolute difference in cell area.
The method comprises the following specific steps:
step 1: giving a time window with the length of 3 sampling intervals, sliding reversely from the last frame when the right side of the time window is at the starting position of the trackWhen intersecting, if the corresponding frame is the k-th frame, the intersecting track will be associated with other tracks ending in the time window (from the k-3 rd frame to the k-1 th frame). If there is a corresponding track candidate in the (k-1) th frame (i.e. the track ends in the (k-1) th frame) and the constraint condition of maximum moving distance between frames is satisfied, the maximum one is selected according to the similarity criterion 1 to be associated with the track candidate. Otherwise, go to step 2.
Step 2: excluding step 1 correlatedIf it isNon-null and corresponding track candidates in the k-2, k-3 frame (i.e., the track ends in the k-2, k-3 frame) and satisfying the maximum moving distance constraint between frames, the largest one is selected to be associated with according to the similarity criterion 1.
And step 3: excluding steps 1,2 already associatedIf it isComplete track of non-empty and adjacent (meeting the constraint of maximum moving distance between frames)Similarity standard 2 calculation is carried out on the k, k-1 frame, if the similarity value is larger than a given threshold value, the flight path x is calculatediIncorporated into flight pathCorresponding to cell division.
And 4, step 4: excluding steps 1,2, 3 already associatedIf it isIf the initial track is not empty, the initial track (and the track life is at least 3 sampling intervals) is considered as a formal track, otherwise, the track is removed.
The technology provided by the invention has the following characteristics:
1) a joint tracking method of multi-cell data association and state estimation based on a label ant colony is provided, and the data association and the state estimation are carried out in parallel and interactively.
2) The matching construction problem based on the label ant colony is different from a general 1-1 matching problem, redundant candidate ant colony measurement can be processed, the candidate ant colony measurement position corresponding to the optimal matching is continuously updated through the ant colony foraging behavior, and the matched candidate ant colony measurement is dynamically changed.
3) The invention provides a new matching objective function, namely OSPA-T, which comprehensively considers potential, position and label matching errors.
4) The invention can extract the spectrum coefficient of the cell by using the trajectory pheromone, and estimate the state of the cell by using the food pheromone.
5) Comparative patent 1ZL201610457030.4 discloses a multicellular automatic tracking method based on tagged multi-bernoulli filters; a comparative patent 2zl201810585820.x discloses a multi-bernoulli random finite ant colony multi-cell tracking method; comparative patent 3ZL201810815283.3 discloses a double-layer multi-bernoulli random finite ant colony multi-cell tracking method; the invention relates to a multi-cell tracking method integrating data association and state estimation based on ant colony elicitation. The differences between the invention and the compared patents 1,2 and 3 are that: the data association and the parameter estimation are processed in a combined way, and the adopted theories, technologies and methods are completely different. As shown in Table 1 below, the precision rate and recall rate of cell division are significantly improved in the present invention compared with those of the comparative patents 1,2 and 3.
TABLE 1 Split event Performance comparison (statistical based on 10 simulation results)
Evaluation indexes are as follows:
where TP indicates the number of correct cell division events detected, FP indicates the number of false detections of cell division events (false alarms), and FN indicates the number of undetected cell division events.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, and simplifications are intended to be included in the scope of the present invention.

Claims (3)

1. The combined multi-cell tracking method based on the label ant colony is characterized by comprising the following steps:
multi-bernoulli random finite set definition and its approximation:
a finite set of multi-bernoulli randoms: the multi-Bernoulli random finite set X is a single Bernoulli random finite set X consisting of a group of a fixed number M(ζ)(1.. said., M) and each single bernoulli random finite set X(ζ)Can use its existence probability r(ζ)E (0,1) and its corresponding probability density function pi(ζ)To indicate that, then, a multi-bernoulli random finite set X can be used with a bernoulli parameter setTo represent; label multi-Bernoulli random finite set available { (r)(ζ),π(ζ)) ζ ∈ Ψ } represents, where Ψ represents a set of indices, to which a label is assigned if a single bernoulli component returns a non-empty set;
label multi-bernoulli random finite set approximation: the finite set of tags, i.e. the population of tagged Bernoulli ants, can be approximated byTherein, ΨaA set of ant colony indices is represented,indicating label ant colonyThe probability of the existence of (a) is,indicating label ant colonyA discrete probability density distribution ofIf the value is larger than a certain threshold value, the ant colony is considered to survive and is connected with a cell labelAre associated with whereinDefining as identity mapping from the ant colony index set to the cell label; given a tag ant colonyProbability of its existenceCan be calculated as
Where s is an area integral variable, g(s) is a heuristic likelihood function, τ(ζ)As a tag ant colonyCorresponding pheromone field, R(ζ)As a tag ant colonyOf the area of influence；
Cell frame-to-frame matching problem definition:
representing the estimated m cell locations at the k-th frame,representing the n cell candidate sets obtained at frame k +1, a bipartite graph G ═ (U, V, E) was constructed in which, e denotes the set of edge matching hypotheses from U to V, and the problem of inter-frame matching translates to
And isWherein D is(C)(. cndot.) represents a cost function for the premise of matching hypothesis C, f (-) represents the mapping of matching hypotheses from U to V, f-1() represents the projection of f, |, represents the potential of some set;
the cost function D uses the optimal path sub-pattern assignment (OSPA-T), i.e.: given two sets of labeled sets X and Y, the number of elements is m and n, respectively, (X { (X)1,l1),...,(xm,lm) Denotes the set of estimated labeled l cell states x of the previous frame, Y { (Y)1,s1),...,(yn,sn) Denotes the subset of candidate metrics y with labels s in the matching hypothesis corresponding to the current frame, OSPA-T is defined as OSPA-T if m ≦ n
Wherein d isc((x, l), (y, s)) -min (c, d ((x, l), (y, s))) represents the intercept distance, the parameters c and p represent the positive sensitivity coefficient (both greater than zero) for the difference in the number of elements of the two sets and the difference in the tagged state variables, respectively, ψnRepresenting a set of feasibility perturbations on set Y,. psi (i) representingnOf (a), a base distance d ((x, l), (y, s)) ═ d (x, y)p′+d(l,s)p′)1/p′P 'represents a base distance order parameter, d (x, y) represents a p' norm distance between two states x, y, d (l, s) represents a label error, d (l, s) equals 0 if l equals s, otherwise d (l, s) equals λ, λ ∈ [0, c ]](ii) a If m > n, there is Dp,c(X,Y)＝Dp,c(Y,X)；
Candidate set generation based on label-free scout ant colony
In the (k + 1) th frame, a given scout ant colony is initially randomly distributed in the current image area, a new ant dynamics system is introduced for modeling the behavior of the scout ant, namely, the scout ant dynamics system gradually evolves from chaotic behavior to deterministic behavior, so that the possible area of the food source is found; the kinetic behavior of a scout ant is defined as follows
Wherein the content of the first and second substances,represents the chaos movement variable of the scout ant during the t iteration, haExpressing the ant self-organizing factor, the value range is between 0 and 1,representing the status of the scout ant at the t-th iteration, parameter ψdIndicate ants inSearch range of search space, parameter VaRepresenting different regions of the control search space, a, b being constants, pa(t-1) represents the optimal solution obtained by the scout ant and the neighbor ants thereof in the previous t-1 iterations;
representing scout antSet of neighboring ants at the t-th iteration, assuming scout antsAnd the current state and the optimal state of the former t-1 iterations of the neighboring ants are known, then the ant is reconnaissanceThe optimal state obtained in the previous t iterations is
Wherein, the symbol V-shaped represents the large operation,representing an inversion operation on a likelihood function g defined as
Wherein, IlRepresenting intensity values, B, of the normalized gray-scale image at pixel lqRepresenting a set of pixels, N, comprised by a square region centred on a pixel q(q)A neighboring pixel set of a pixel q is represented, a symbol | · | represents the number of elements in the set, and a symbol ^ represents the small calculation; on the t-th iteration, if ant is detectedAt pixel q, then
Regarding ant states of the ant colony set in two successive iterations as a two-state setAndthen the OSPA-T is reduced to an optimal sub-modal allocation (OSPA) distanceThus, when ma≤naWhen there is
If ma＞naDefinition of
Step 1: initialization: given a plurality of groups of scout ant colonies, scout the chaotic mobile variable y in the dynamics behavior of the anta(0) Self-organizing factor haReconnaissance of initial state of antSearch scope parameter psidDifferent region parameters V of the search spaceaConstants a, b, etc. are known;
step 2: for each group of scout ant colony, each scout ant moves according to a dynamic behavior model, the likelihood function value of the corresponding pixel where the scout ant is located is sensed according to the definition of the likelihood function, and information exchange is carried out between the likelihood function value and the adjacent scout ants to obtain the optimal state obtained by the current iteration;
and step 3: if the pixel position of the detective ant is the position area where the possible cell is detected, setting the corresponding likelihood function as a very small value;
and 4, step 4: calculating the optimal sub-mode distribution distance between the current iteration scouting ant colony state set and the last iteration scouting ant colony state setIf the difference is smaller than a certain threshold value, the scouting work of the scout ant colony is terminated, and then a plurality of scout ant colonies are generated through cluster reconstruction;
and 5: repeating the steps 2-4 until no new reconnaissance ant colony is generated; the center of each generated scout ant colony is used as the centerThus, n candidate measurements are formed
2. The tag ant colony based combined multicellular tracking method as recited in claim 1, further comprising: matching construction and parameter estimation joint tracking based on label ant colony
Set label multi-Bernoulli random finite set parameter { (r)(ζ),π(ζ)) ζ ∈ Ψ } and tag set of multi-bernoulli ant group parametersThere is a one-to-one correspondence, and the tag colony of Bernoulli ants has a one-to-one correspondence with the cell, i.e.
Assuming that the tag is ζ ant colony, the tag will move from the position of the previous frame to the position of the next frame with a survival probability, except that the uniqueness of the tag is unchanged, the survival probability is defined as:
where H, W denote the height and width of the current frame image,indicating the shortest height and width direction distance from the center of the tag ant colony to the image boundary at the k-th frame,representing the existence probability of the tag ant colony in the k frame;
similarly, the probability of the tag ant colony splitting at the next frame k +1 is defined as
Wherein exp (. cndot.) represents an exponential function,respectively represent cellsThe resulting contour aspect ratio is estimated at the k-th frame and the initial frame,respectively represent cellsAt the average intensity of the k-th and initial frames,υ is a regulation factor between 0 and 1,indicates the corresponding cellThe size of the local window area of (a),represents the estimated cells at the k frameThe area size;
based on the above definition, the tag ant colony-based interframe matching and parameter estimation integrated method is described as follows:
step 1: initialization: assuming there were m cell estimates in the previous frame k For the estimated location of cell i, its corresponding set of tagged Bernoulli ant population parameters can be expressed asFor each Bernoulli colony, the colony scales are allGeneration of n candidate measurement sets from unlabeled scout ant colonies Representing candidate metrology j locations;
step 2: bernoulli ant colony for any labelOptionally one of the labeled ants (consistent with the ant colony label) randomly generating two random numbers kappaSE (0,1) and kME (0,1), if:
(1)：the tag ant can survive from the previous frame and estimate the position from the corresponding cellStarting with, selecting candidate metricsHas a probability of
Wherein 1 isY(X) denotes an inclusion function, ifThen equals 1, otherwise 0;is shown asA subset of candidate measurements corresponding to the estimated location of each cell,is shown in the trackThe intensity of the trace pheromone, theta (·) represents the identity function of the trace pheromone, which is associated with the cellCorrelation;represents a heuristic function and hasd (,) represents a distance function, α1,β1Representing a relative importance coefficient;
(2)：the ant can survive from the last frame and should have the possibility of cell division, so that the tag ant is duplicated into two identical tag ants, and the positions of the two identical tag ants are estimated successively from the corresponding cellsStarting with, selecting different candidate measurementsHas a probability of
(3)：OrThe ant is still, which indicates the detail corresponding to it in the next frameCells may disappear;
when the label ant decides according to (1) or (2), the passing track is followedUpper release of a certain amount of pheromone:
where p represents the pheromone residual coefficient,indicating that the current frame is k +1 corresponding label Bernoulli ant colonyThe resulting probability of presence after the last iteration update,representing cellsThe area of influence of (a);
and step 3: after the m label Bernoulli ant colonies complete corresponding decisions according to the step 2, forming a matching hypothesis C from U to V, and calculating corresponding OSPA-T values;
and 4, step 4: according to the step 2-3, carrying outIs circulated secondarily inIn the secondary loop, the best matching hypothesis C of the iteration is obtained, and the corresponding candidate set is expressed asTo renThe labeled Bernoulli ant colony obtained according to step 2Starting cell state estimation, i.e. foraging; if a foraging ant is on pixel p, the probability that it moves to pixel q is defined as
Wherein alpha is2,β2Representing the relative importance coefficient, N(p)Representing a set of neighboring pixels of the pixel p,representing the intensity of the food pheromone at the current frame k +1 pixel q; following the above decision, the tag ant releases a certain amount of pheromone on pixel q at the same time
Wherein epsilon1Is a threshold coefficient;
when labeled Bernoulli ant colonyAfter all ants finish the foraging decision, the corresponding food pheromone field is updated
Wherein the content of the first and second substances,is shown in the imageThe total pheromone input on the pixel q,represents the total pixel spread input over pixel q, defined as
Wherein D represents a diffusion constant coefficient, the value range is (0,1), kappa is a control constant coefficient,represents pixels q anddistance between, RqRepresenting the area of influence of pixel q;
obtaining the label Bernoulli ant colony by using the obtained food pheromone field and a heuristic function after multiple iterationsBernoulli parameter ofApproximation
Wherein the content of the first and second substances,representing the probability density dispersion distribution of the foraging label ant colony of the current frame k +1,representing antsState of (1)The weight corresponding to the weight of the corresponding weight,representing a signature Bernoulli ant colonyThe number of ants in (1); for the food pheromone field, three simple processes of binarization, morphology and filling are carried out to obtain the outline and the position of the corresponding cell of the candidate set
And 5: for the best matching hypothesis C obtained by the current iteration, the corresponding candidate set position, the track pheromone field and the food pheromone field are subjected to global updating
Wherein Q is1，Q2In order to enhance the constant for the pheromone,representing a candidate set after the position corresponding to the best matching hypothesis C obtained by the current iteration is updated;
step 6: repeating the steps 2-5 until the convergence condition is met(ii) a Meanwhile, the food pheromone field obtained by the obtained optimal matching iteration is subjected to three simple processes of binarization, morphology and filling, and if the obtained labeled ant colony is obtainedProbability of existenceThe contour and position estimation of the corresponding cell can be obtained;
extracting a track pheromone field of the obtained optimal matching between frames, keeping the identity characteristics of the track pheromone, and forming a cell lineage tree through frame-frame sequential matching;
regarding unmatched candidate measurement as a new item which may appear in the current frame, correspondingly generating mutually independent tag Bernoulli ant colony, constructing a corresponding food pheromone field according to the step 4, and if the existing probability of the new tag ant colony is not lower than 0.5, extracting the outline and position estimation of the corresponding cell;
the positions obtained by the multiple label Bernoulli ant colonies are estimated to be close and the mutual distance is smaller than a certain threshold value, the label Bernoulli ant colony with high existence probability is reserved, and other label Bernoulli ant colonies meeting the conditions are directly removed and are not considered any more; meanwhile, for updating the label, the label which is the first to appear is given to the label Bernoulli ant colony with high existence probability.
3. The tag ant colony based joint multi-cell tracking method as claimed in claim 1, further comprising four-stage based flight path recovery:
the similarity standard for the four-stage based track recovery is as follows:
similarity standard 1: respectively representing flight pathsCell states corresponding to birth and end times, for both tracksAndif it isThe ending time precedesThe similarity criterion 1 is defined as
Wherein R is-Representing a set of tracks meeting the constraint condition of maximum moving distance between frames, and any track thereofThe ending time precedes Representing corresponding tracksThe area of the cells at the time of birth is estimated,presentation pairTrack of responseEstimating the area of the cell at the end moment, wherein n represents the intersection of the areas of the two cells, and U represents the sum of the areas of the two cells;
similarity criterion 2: for flight pathThe state of the cell corresponding to the birth time k isFor flight pathThe cell states at times k and k-1 are respectivelyAndthe similarity criterion 2 is defined as
Wherein, Ch(. and C)w(. h) represents the lengths of the major and minor axes of the cell contour, respectively, Δ Ch(. phi.) and Δ Cw(-) represents the absolute value of the difference in length of the major and minor axes of the cell contour, respectively, and Δ A (·) represents the absolute value of the difference in cell area;
the method comprises the following specific steps:
stage 1: giving a time window with the length of 3 sampling intervals, sliding reversely from the last frame when the right side of the time window is at the starting position of the trackWhen intersecting, if the corresponding frame is the k-th frame, the intersecting track is associated with other tracks ending in the time window (from the k-3 th frame to the k-1 th frame); if the k-1 frame has a corresponding track candidate (namely the track is finished in the k-1 frame), and the constraint condition of the maximum moving distance between the frames is met, selecting the maximum one to be associated with according to the similarity standard 1; otherwise, entering stage 2;
and (2) stage: excluding phase 1 correlatedIf it isIf the space is not empty and the corresponding track candidate exists in the (k-2, k-3) th frame (namely the track is ended in the (k-2, k-3) th frame) and the constraint condition of the maximum moving distance between the frames is met, selecting the maximum one to be associated with the maximum one according to the similarity standard 1;
and (3) stage: excluding stages 1,2 already associatedIf it isComplete track of still non-empty and neighboring (meeting the constraint of maximum moving distance between frames)Similarity standard 2 calculation is carried out on the k, k-1 frame, if the similarity value is larger than a given threshold value, the flight path is determinedIncorporated into flight pathCorresponding cell division;
and (4) stage: excluding stages 1,2, 3 already associatedIf it isIf the initial track is not empty, the initial track (and the track life is at least 3 sampling intervals) is considered as a formal track, otherwise, the track is removed.
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CN111738399A (en) * 2020-08-13 2020-10-02 常熟理工学院 Heuristic ant colony track recovery method
CN111914211A (en) * 2020-07-30 2020-11-10 深圳大学 Method and device for generating multi-Bernoulli distribution of new target label
CN113011082A (en) * 2021-02-07 2021-06-22 山东大学 Lithium battery SOC prediction method for optimizing particle filtering by improving ant colony algorithm
CN115273978A (en) * 2022-08-29 2022-11-01 西安交通大学 Method for obtaining splicing epigenetic code suitable for multilayer pedigree tree
CN116543015A (en) * 2023-04-26 2023-08-04 常熟理工学院 Method and system for constructing cell lineage tree based on deep learning

Citations (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102156478A (en) * 2010-12-28 2011-08-17 北京航空航天大学 Integrated attitude determination method based on ant colony unscented particle filter algorithm
US20120084235A1 (en) * 2010-09-30 2012-04-05 Massachusetts Institute Of Technology Structured prediction model learning apparatus, method, program, and recording medium
US20120114723A1 (en) * 2004-10-01 2012-05-10 Victor Bruce Steward One step fire ant control
CN102999922A (en) * 2012-11-19 2013-03-27 常熟理工学院 Multi-cell automatic tracking method and system based on plurality of task ant systems
CN103150562A (en) * 2013-03-22 2013-06-12 常熟理工学院 Ant colony cell tracking system based on premise of image background extraction
CN103955946A (en) * 2013-08-16 2014-07-30 常熟理工学院 Ant colony neighbor cell tracking system based on cooperation and competition mode and application thereof
CN104063880A (en) * 2014-06-12 2014-09-24 常熟理工学院 PSO based multi-cell position outline synchronous accurate tracking system
CN105279768A (en) * 2015-02-03 2016-01-27 常熟理工学院 Variable density cell tracking method based on multi-mode ant colony system
CN106097394A (en) * 2016-06-22 2016-11-09 常熟理工学院 The many cells automatic tracking method of many bernoulli wave filter based on tape label
CN106408594A (en) * 2016-09-28 2017-02-15 江南大学 Video multi-target tracking method based on multi-Bernoulli characteristic covariance
CN107871156A (en) * 2017-11-02 2018-04-03 常熟理工学院 Ant colony many cells tracking system based on pheromones prediction
CN108961309A (en) * 2018-06-08 2018-12-07 常熟理工学院 More bernoulli stochastic finite ant colony many cells trackings
CN109118518A (en) * 2018-07-24 2019-01-01 常熟理工学院 Double-deck more bernoulli stochastic finite ant colony many cells trackings
CN109146881A (en) * 2018-10-09 2019-01-04 常熟理工学院 A kind of ant colony aggregation tracking cell system based on gesture estimation auxiliary

Patent Citations (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20120114723A1 (en) * 2004-10-01 2012-05-10 Victor Bruce Steward One step fire ant control
US20120084235A1 (en) * 2010-09-30 2012-04-05 Massachusetts Institute Of Technology Structured prediction model learning apparatus, method, program, and recording medium
CN102156478A (en) * 2010-12-28 2011-08-17 北京航空航天大学 Integrated attitude determination method based on ant colony unscented particle filter algorithm
CN102999922A (en) * 2012-11-19 2013-03-27 常熟理工学院 Multi-cell automatic tracking method and system based on plurality of task ant systems
CN103150562A (en) * 2013-03-22 2013-06-12 常熟理工学院 Ant colony cell tracking system based on premise of image background extraction
CN103955946A (en) * 2013-08-16 2014-07-30 常熟理工学院 Ant colony neighbor cell tracking system based on cooperation and competition mode and application thereof
CN104063880A (en) * 2014-06-12 2014-09-24 常熟理工学院 PSO based multi-cell position outline synchronous accurate tracking system
CN105279768A (en) * 2015-02-03 2016-01-27 常熟理工学院 Variable density cell tracking method based on multi-mode ant colony system
CN106097394A (en) * 2016-06-22 2016-11-09 常熟理工学院 The many cells automatic tracking method of many bernoulli wave filter based on tape label
CN106408594A (en) * 2016-09-28 2017-02-15 江南大学 Video multi-target tracking method based on multi-Bernoulli characteristic covariance
CN107871156A (en) * 2017-11-02 2018-04-03 常熟理工学院 Ant colony many cells tracking system based on pheromones prediction
CN108961309A (en) * 2018-06-08 2018-12-07 常熟理工学院 More bernoulli stochastic finite ant colony many cells trackings
CN109118518A (en) * 2018-07-24 2019-01-01 常熟理工学院 Double-deck more bernoulli stochastic finite ant colony many cells trackings
CN109146881A (en) * 2018-10-09 2019-01-04 常熟理工学院 A kind of ant colony aggregation tracking cell system based on gesture estimation auxiliary

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
MINGLI LU 等: "A Novel Multiple Adjacent Cell Tracking Approach Based on Pheromone Prediction of Ant Colony", 《2017 INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION AND INFORMATION SCIENCES》 *
MINGLI LU 等: "Ant Colony Pheromone Field Evolution Based Parameter Estimator Approach for Adjacent Multiple Cell Tracking", 《PROCEEDINGS OF THE 37TH CHINESE CONTROL CONFERENCE》 *
S.BARATH KUMAR 等: "Ant-Colony-based Algorithm for Multi-Target Tracking in Mobile Sensor Networks", 《INTERNATIONAL JOURNAL OF COMPUTER APPLICATIONS》 *
刘伟峰 等: "基于OSPA距离的航迹关联方法", 《航空学报》 *
蒋冬梅 等: "基于蚁群系统的多细胞跟踪方法及其LabVIEW实现", 《中国优秀硕士学位论文全文数据库 信息科技辑》 *
陈庆兰 等: "基于粒子群的多细胞状态估计技术", 《常熟理工学院学报（自然科学）》 *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111474149A (en) * 2020-04-10 2020-07-31 复旦大学附属中山医院 Dynamic assessment method for mitochondria
CN111474149B (en) * 2020-04-10 2023-08-08 复旦大学附属中山医院 Dynamic evaluation method for mitochondria
CN111914211A (en) * 2020-07-30 2020-11-10 深圳大学 Method and device for generating multi-Bernoulli distribution of new target label
CN111738399A (en) * 2020-08-13 2020-10-02 常熟理工学院 Heuristic ant colony track recovery method
CN113011082A (en) * 2021-02-07 2021-06-22 山东大学 Lithium battery SOC prediction method for optimizing particle filtering by improving ant colony algorithm
CN113011082B (en) * 2021-02-07 2022-07-12 山东大学 Lithium battery SOC prediction method for optimizing particle filtering by improving ant colony algorithm
CN115273978A (en) * 2022-08-29 2022-11-01 西安交通大学 Method for obtaining splicing epigenetic code suitable for multilayer pedigree tree
CN116543015A (en) * 2023-04-26 2023-08-04 常熟理工学院 Method and system for constructing cell lineage tree based on deep learning

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