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CN112200836B - Multi-cell tracking method and system based on self-adjusting foraging behavior of ants - Google Patents

Multi-cell tracking method and system based on self-adjusting foraging behavior of ants Download PDF

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CN112200836B
CN112200836B CN202011040382.2A CN202011040382A CN112200836B CN 112200836 B CN112200836 B CN 112200836B CN 202011040382 A CN202011040382 A CN 202011040382A CN 112200836 B CN112200836 B CN 112200836B
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鲁明丽
徐本连
吴妹英
施健
刘静
王伟
朱培逸
吴迪
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Suzhou Institute Of Technology
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Abstract

The invention discloses a multi-cell tracking method and system based on ant self-adjusting foraging behavior. After a cell image sequence is input, predicting a current frame according to an iteration result of an ant colony and an pheromone field of a previous frame to form a Gaussian ant colony and a Gaussian pheromone field; constructing an pheromone field by utilizing three strategies, namely, ant colony foraging range limitation, an ant colony resampling mechanism and an ant colony foraging stopping criterion, under an exponential form-based ant working mode; and then calculating the existence probability of the ant colony, fusing similar ant colonies, and extracting the cell state by considering the ant colony with the existence probability greater than a threshold value and a corresponding Gaussian pheromone field to realize accurate tracking of multiple cells.

Description

基于蚂蚁自调整觅食行为的多细胞跟踪方法及系统Multi-cell tracking method and system based on self-adjusting foraging behavior of ants

技术领域technical field

本发明属于多目标跟踪领域，更具体的涉及基于蚂蚁自调整觅食行为的多细胞跟踪系统。The invention belongs to the field of multi-target tracking, and more particularly relates to a multi-cell tracking system based on the self-adjusting foraging behavior of ants.

背景技术Background technique

细胞作为生物体基本的结构和功能单位，它的增殖、分化和迁移不仅是任何有机生命的胚胎发育、进化和生命维持必不可少的环节还与疾病的产生与发展有着不可分割的联系，例如，大部分癌症是由于癌细胞从初始的发病组织转移到周围健康组织而导致的癌症扩散。因此，对细胞行为分析的研究在很多领域都是非常有价值的。通过分析细胞运动的过程来获得细胞的形状、数目、速度、轨迹和生长周期等特征信息，可以对细胞进行定性和定量分析，可见，对细胞动力学行为的研究对诊断和治疗疾病、提高药物研制效率等都有着不可预估的重要意义。传统的人工跟踪仍然是实验室目前最常用的跟踪方法，但这种方法不仅耗时、容易出错，而且对研究人员的专业知识和临床经验要求高。因此细胞自动跟踪方法的研究成为了一个急需解决的问题。As the basic structural and functional unit of an organism, the proliferation, differentiation and migration of cells are not only an indispensable link in the embryonic development, evolution and life maintenance of any organic life, but also have an inseparable connection with the generation and development of diseases, such as , the majority of cancers are the spread of cancer due to the metastasis of cancer cells from the original diseased tissue to surrounding healthy tissue. Therefore, the study of cell behavior analysis is very valuable in many fields. By analyzing the process of cell movement, characteristic information such as cell shape, number, speed, trajectory and growth cycle can be obtained, and qualitative and quantitative analysis of cells can be carried out. Development efficiency and so on have unpredictable significance. Traditional manual tracking is still the most commonly used tracking method in laboratories, but this method is not only time-consuming and error-prone, but also requires a high degree of researcher expertise and clinical experience. Therefore, the research of automatic cell tracking method has become an urgent problem to be solved.

显微图像序列细胞的跟踪面临许多困难，比如低信噪比、细胞边界模糊、细胞变形，数目时变及细胞迁移运动的速度和方向突然改变，导致跟踪的失败等。近年来学者们提出的自动跟踪的方法大多数是针对特定数据，而且跟踪精度对细胞分割的结果依赖较强，对于复杂情形下细胞跟踪的精度不高。目前针对细胞图像序列中形变、运动特性各异及数目时变等细胞跟踪的研究理论和方法较少。本发明旨在解决形变、运动特性各异及数目时变等等多细胞跟踪难题，利用蚂蚁自调整觅食行为构建信息素场，最终实现复杂情形下多细胞的精确跟踪。The tracking of cells in microscopic image sequences faces many difficulties, such as low signal-to-noise ratio, blurred cell boundaries, cell deformation, time-varying numbers, and sudden changes in the speed and direction of cell migration, which lead to the failure of tracking. Most of the automatic tracking methods proposed by scholars in recent years are for specific data, and the tracking accuracy is strongly dependent on the results of cell segmentation, and the accuracy of cell tracking in complex situations is not high. At present, there are few research theories and methods for cell tracking such as deformation, different motion characteristics and time-varying number of cell image sequences. The invention aims to solve the problems of multi-cell tracking such as deformation, different motion characteristics and time-varying numbers, etc., and utilizes the self-adjusting foraging behavior of ants to construct a pheromone field, and finally realizes the accurate tracking of multi-cells in complex situations.

发明内容SUMMARY OF THE INVENTION

1、本发明的目的。1. Purpose of the present invention.

本发明为了解决现有技术中对于数目时变、变形、运动特性各异和近邻多细胞跟踪难题，提出了一种基于蚂蚁自调整觅食行为的多细胞跟踪系统。The invention proposes a multi-cell tracking system based on the self-adjusting foraging behavior of ants in order to solve the problems of time-varying number, deformation, different motion characteristics and multi-cell tracking of neighbors in the prior art.

2、本发明所采用的技术方案。2. The technical solution adopted in the present invention.

本发明公开了一种基于蚂蚁自调整觅食行为的多细胞跟踪方法，包括如下步骤：The invention discloses a multi-cell tracking method based on the self-adjusting foraging behavior of ants, comprising the following steps:

蚁群及信息素场双预测步骤，输入原始图像，基于前一帧蚁群及结果信息素场，利用高斯模型对当前帧蚁群及信息素场进行预测；The ant colony and pheromone field double prediction step, input the original image, and use the Gaussian model to predict the current frame ant colony and pheromone field based on the previous frame ant colony and the resulting pheromone field;

蚂蚁自调整觅食步骤，在基于指数形式的蚂蚁工作模式下利用三种策略，即限定蚁群觅食范围、蚁群重采样机制、蚁群觅食停止准则构建信息素场，实现形变、数目变化、运动状态不定和近邻细胞跟踪；Ants self-adjust their foraging steps, and use three strategies under the exponential-based ant work mode, namely, limited ant colony foraging range, ant colony resampling mechanism, and ant colony foraging stop criterion to construct a pheromone field to achieve deformation, number of Changes, variable motion, and neighbor cell tracking;

细胞状态估计步骤，基于结果信息素场和启发式函数计算每个子蚁群的存在概率，删除存在概率小于阈值的蚁群，融合相似蚁群并考虑存在概率大于阈值的蚁群进行多细胞状态估计；The cell state estimation step is to calculate the existence probability of each sub-ant colony based on the resulting pheromone field and heuristic function, delete the ant colonies whose existence probability is less than the threshold, fuse similar ant colonies and consider the ant colonies whose existence probability is greater than the threshold for multi-cell state estimation ;

其中蚂蚁自调整觅食步骤，具体为：The ants self-adjust foraging steps, specifically:

1)输入细胞图像序列，构建信息素场中的基于指数形式的蚂蚁工作模式；蚂蚁的觅食行为限定在规定范围内并根据概率选择邻域内像素进行搜索；假如第v组蚁群中的蚂蚁l处于像素(i′,j′)所在位置，考虑指数形式对变量的变化比较敏感，则该蚂蚁选择其可用邻域内某一像素(i,j)的概率为：1) Input the cell image sequence to construct the exponential-based ant working mode in the pheromone field; the foraging behavior of the ants is limited to a specified range and the pixels in the neighborhood are selected according to the probability to search; if the ants in the vth group of ants are l is at the position of the pixel (i', j'), considering that the exponential form is more sensitive to changes in variables, the probability of the ant selecting a pixel (i, j) in its available neighborhood is:

Figure GDA0003200753810000021
Figure GDA0003200753810000021

其中

Figure GDA0003200753810000022
为第v组蚁群像素(i,j)上第t次迭代的信息素，ηi,j是像素(i,j)的启发式函数；α和β是信息素
Figure GDA0003200753810000023
和启发式函数ηi,j之间的调节参数，Ω(i′,j′)是像素(i′,j′)的可用邻域集合；Ω(i′,j′)是限定蚂蚁觅食范围与像素(i′,j′)邻域的交集；in
Figure GDA0003200753810000022
is the pheromone of the t-th iteration on the vth group of ant colony pixels (i, j), η i, j is the heuristic function of the pixel (i, j); α and β are the pheromone
Figure GDA0003200753810000023
and the heuristic function η i,j , Ω(i′,j′) is the set of available neighborhoods for the pixel (i′,j′);Ω(i′,j′) is the limit of ant foraging The intersection of the range and the neighborhood of the pixel (i', j');

启发式函数ηi,j定义为

Figure GDA0003200753810000024
其中ΔIi,j和ΔAi,j分别表示像素(i,j)邻域内的像素强度差分和平均值；λ是调节系数，决定ΔIi,j和ΔAi,j两个变量对启发式函数值的影响，定义为λ＝Imean/Imax，其中Imean和Imax分别表示当前帧像素的平均强度和最大强度；γ和κ都是调节系数保证启发式函数值在区间[0，1]之间变化；如果图像背景的启发式函数值大于前景的，则γ＝1，否则γ＝2；同样如果启发式函数值大于1，则κ＝1，否则，κ＝0；The heuristic function η i,j is defined as
Figure GDA0003200753810000024
where ΔI i,j and ΔA i,j represent the pixel intensity difference and average value in the neighborhood of pixel (i,j), respectively; λ is the adjustment coefficient, which determines the heuristic function of the two variables ΔI i,j and ΔA i,j The influence of the value is defined as λ=I mean /I max , where I mean and I max represent the average intensity and maximum intensity of the current frame pixel respectively; γ and κ are both adjustment coefficients to ensure that the heuristic function value is in the interval [0, 1 ]; if the heuristic function value of the image background is greater than that of the foreground, then γ=1, otherwise γ=2; also if the heuristic function value is greater than 1, then κ=1, otherwise, κ=0;

2)当所有蚂蚁完成搜索后，对像素(i，j)上的信息素量进行更新

Figure GDA0003200753810000031
其中
Figure GDA0003200753810000032
为第ν组蚁群第t次迭代在像素(i，j)上的信息素量，ρ(0＜ρ＜1)表示信息素残留系数，
Figure GDA0003200753810000033
为第t-1次迭代蚂蚁l在像素(i，j)上释放的信息素量；2) When all ants complete the search, update the amount of pheromone on the pixel (i, j)
Figure GDA0003200753810000031
in
Figure GDA0003200753810000032
is the amount of pheromone on the pixel (i, j) in the t iteration of the νth group ant colony, ρ(0<ρ<1) represents the residual pheromone coefficient,
Figure GDA0003200753810000033
is the amount of pheromone released by the ant l on the pixel (i, j) in the t-1th iteration;

3)当第v组蚁群中所有蚂蚁完成第t次迭代后，对第v组信息素场进行高斯拟合，得到第v组高斯信息素场，信息素变量服从均值为

Figure GDA0003200753810000034
协方差为
Figure GDA0003200753810000035
的高斯分布
Figure GDA0003200753810000036
其中τ(ν)(t)为第t次迭代后第v组高斯信息素场，τ(t)表示信息素变量，
Figure GDA0003200753810000037
和
Figure GDA0003200753810000038
分别为第t次迭代后第v组高斯信息素场信息素量的均值及协方差；3) When all the ants in the vth group of ants complete the tth iteration, perform Gaussian fitting on the vth group pheromone field to obtain the vth group Gaussian pheromone field, and the pheromone variables obey the mean of
Figure GDA0003200753810000034
The covariance is
Figure GDA0003200753810000035
Gaussian distribution of
Figure GDA0003200753810000036
where τ (ν) (t) is the v-th Gaussian pheromone field after the t-th iteration, and τ(t) represents the pheromone variable,
Figure GDA0003200753810000037
and
Figure GDA0003200753810000038
are the mean and covariance of the pheromone amount of the vth group of Gaussian pheromone field after the tth iteration;

4)计算第t次迭代后第ν组高斯信息素场和第t-1次迭代后第v组高斯信息素场之间的KL距离Dτ(t)，如果Dτ(t)大于阈值ε，则对第t次迭代后第v组蚁群进行高斯重采样，得到高斯蚁群

Figure GDA0003200753810000039
为第t+1次迭代第ν组蚁群的初始分布，其中x(v，l)(t+1)表示第t+1次迭代第ν组蚁群蚂蚁l的状态，而且x(v，l)(t+1)服从均值为
Figure GDA00032007538100000310
协方差为
Figure GDA00032007538100000311
的高斯分布，x(ν，l)(t+1)：
Figure GDA00032007538100000312
同时根据第t次迭代后第ν组高斯信息素场重构第y组蚁群在第t+1次迭代中的蚂蚁觅食范围；4) Calculate the KL distance D τ (t) between the ν-th Gaussian pheromone field after the t-th iteration and the v-th Gaussian pheromone field after the t-1-th iteration, if D τ (t) is greater than the threshold ε , then Gaussian resampling is performed on the vth group of ant colonies after the t-th iteration, and the Gaussian ant colony is obtained.
Figure GDA0003200753810000039
is the initial distribution of the νth group ant colony at the t+1th iteration, where x (v, l) (t+1) represents the state of the νth group ant colony l at the t+1th iteration, and x (v, l) (t+1) obeys the mean
Figure GDA00032007538100000310
The covariance is
Figure GDA00032007538100000311
Gaussian distribution of , x (ν, l) (t+1):
Figure GDA00032007538100000312
At the same time, according to the Gaussian pheromone field of the νth group after the tth iteration, the ant foraging range of the yth group of ants in the t+1th iteration is reconstructed;

5)继续上述步骤1)-4)，直至Dτ(t)小于阈值ε，达到迭代终止条件。5) Continue the above steps 1)-4) until D τ (t) is less than the threshold ε and the iteration termination condition is reached.

优选的，所述蚁群及信息素场双预测步骤，其具体预测方式如下：Preferably, in the double prediction step of the ant colony and the pheromone field, the specific prediction method is as follows:

1)设定在第k-1帧有Nk-1个细胞，与细胞对应的蚁群及信息素场也有Nk-1个，第y(v＝1，...，Nk-1)组蚁群包含M个蚂蚁，状态表示为

Figure GDA00032007538100000313
服从均值为
Figure GDA00032007538100000314
协方差为
Figure GDA00032007538100000315
的高斯分布
Figure GDA00032007538100000316
其中l表示蚂蚁，xk-1为第k-1帧蚂蚁状态变量，
Figure GDA00032007538100000317
和
Figure GDA00032007538100000318
分别为第k-1帧第y组蚁群蚂蚁状态变量的均值及协方差；第k-1帧第v组蚁群中蚂蚁l的状态
Figure GDA00032007538100000319
预测到第k帧为
Figure GDA00032007538100000320
其中F为状态转移矩阵，
Figure GDA00032007538100000321
表示第k帧第v组蚁群中蚂蚁l的预测状态，服从均值为
Figure GDA0003200753810000041
协方差为
Figure GDA0003200753810000042
的高斯分布
Figure GDA0003200753810000043
xk|k-1表示预测到第k帧的蚂蚁状态变量，
Figure GDA0003200753810000044
其中“∑”表示求和运算，
Figure GDA0003200753810000045
T表示矩阵转置；1) It is assumed that there are N k-1 cells in the k-1th frame, and there are also Nk-1 ant colonies and pheromone fields corresponding to the cells, and the yth (v=1,..., Nk-1 ) group ant colony contains M ants, and the state is expressed as
Figure GDA00032007538100000313
obey the mean
Figure GDA00032007538100000314
The covariance is
Figure GDA00032007538100000315
Gaussian distribution of
Figure GDA00032007538100000316
where l represents the ant, x k-1 is the ant state variable in the k-1th frame,
Figure GDA00032007538100000317
and
Figure GDA00032007538100000318
are the mean and covariance of the state variables of the ants in the yth group ant colony at the k-1th frame, respectively; the state of the ant l in the vth group ant colony at the k-1th frame
Figure GDA00032007538100000319
It is predicted that the kth frame is
Figure GDA00032007538100000320
where F is the state transition matrix,
Figure GDA00032007538100000321
Represents the predicted state of ant l in the vth group of ant colonies in the kth frame, obeying the mean of
Figure GDA0003200753810000041
The covariance is
Figure GDA0003200753810000042
Gaussian distribution of
Figure GDA0003200753810000043
x k|k-1 represents the state variable of the ant predicted to the kth frame,
Figure GDA0003200753810000044
where "∑" represents the summation operation,
Figure GDA0003200753810000045
T represents matrix transpose;

2)假定第k-1帧第ν组信息素场

Figure GDA0003200753810000046
符合均值为
Figure GDA0003200753810000047
协方差为
Figure GDA0003200753810000048
的高斯分布
Figure GDA0003200753810000049
则第y组信息素场预测到第k帧为
Figure GDA00032007538100000410
其中，
Figure GDA00032007538100000411
为第y组第k帧预测信息素场，τk|k-1表示第k帧信息素变量。2) Assume that the νth group pheromone field of the k-1th frame
Figure GDA0003200753810000046
conforming to the mean
Figure GDA0003200753810000047
The covariance is
Figure GDA0003200753810000048
Gaussian distribution of
Figure GDA0003200753810000049
Then the yth group pheromone field predicts the kth frame as
Figure GDA00032007538100000410
in,
Figure GDA00032007538100000411
Predict the pheromone field for the kth frame of the yth group, and τ k|k-1 represents the kth frame pheromone variable.

优选的，所述细胞状态估计步骤的具体方式如下：Preferably, the specific manner of the cell state estimation step is as follows:

1)计算存在概率r(v)：当达到迭代终止条件，第ν组蚁群中所有蚂蚁完成移动后，形成信息素场τ(v)，计算第v组蚁群的存在概率，

Figure GDA00032007538100000412
Figure GDA00032007538100000413
为第ν组信息素场像素
Figure GDA00032007538100000414
上的信息素量，
Figure GDA00032007538100000416
为像素
Figure GDA00032007538100000415
上的启发式函数值，Γ(ν)为当前帧第ν组蚁群对应细胞轮廓内的像素集；1) Calculate the existence probability r (v) : when the iteration termination condition is reached, after all the ants in the νth group ant colony have completed their movement, a pheromone field τ (v) is formed, and the existence probability of the vth group ant colony is calculated,
Figure GDA00032007538100000412
Figure GDA00032007538100000413
is the vth group of pheromone field pixels
Figure GDA00032007538100000414
The amount of pheromone on the
Figure GDA00032007538100000416
for pixels
Figure GDA00032007538100000415
The heuristic function value on , Γ (ν) is the pixel set in the corresponding cell contour of the νth group ant colony in the current frame;

2)当第v组蚁群的存在概率大于预先设定的阈值，则保留第ν组蚁群，否则删除第ν组蚁群；2) When the existence probability of the vth group ant colony is greater than the preset threshold, then keep the nth group ant colony, otherwise delete the nth group ant colony;

3)融合空间相似蚁群后，进行细胞状态估计。3) After fusion of spatially similar ant colonies, cell state estimation is performed.

优选的，将第ν组蚁群的存在概率大于预先设定的阈值设为0.5。Preferably, the existence probability of the nth group of ant colonies is set to be greater than a preset threshold as 0.5.

本发明提出了一种多细胞跟踪系统，包括存储器和处理器，存储器存储有计算机程序，其特征在于；所述处理器执行所述计算机程序时实现所述的方法步骤。The invention provides a multi-cell tracking system, comprising a memory and a processor, wherein the memory stores a computer program, and is characterized in that the processor implements the method steps when executing the computer program.

3、本发明所具有的效果：3. Effects of the present invention:

1)本发明所提出的基于蚂蚁自调整觅食行为的多细胞跟踪系统，在基于指数形式的蚂蚁工作模式下利用三种策略，即，蚁群觅食范围限定、蚁群重采样机制、蚁群觅食停止准则，构建信息素场，能解决形变、运动特性各异、数目时变和近邻等多细胞跟踪问题取得了良好跟踪效果，适用范围较广；1) The multi-cell tracking system based on the self-adjusting foraging behavior of ants proposed by the present invention utilizes three strategies under the ant working mode based on the exponential form, namely, the limited foraging range of the ant colony, the resampling mechanism of the ant colony, the The group foraging stop criterion and the construction of a pheromone field can solve the multi-cell tracking problems such as deformation, different motion characteristics, time-varying number and neighbors, and have achieved good tracking results and have a wide range of applications;

2)本发明所设计的方法跟踪精度高；与基于信息素预测的蚁群多细胞跟踪算法，SMAL博士提出的粒子滤波器细胞跟踪方法及REZA教授提出的多贝努利滤波器及高斯混合PHD滤波器相比，精确率Precision(P)，召回率Recall (R)和F1-测量都得到提升。2) The method designed by the present invention has high tracking accuracy; and the ant colony multi-cell tracking algorithm based on pheromone prediction, the particle filter cell tracking method proposed by Dr. SMAL and the multi-Bernoulli filter and Gaussian mixture PHD proposed by REZA Compared to filters, Precision (P), Recall (R) and F1-measures are all improved.

附图说明Description of drawings

下面结合附图和实施例对本发明进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

图1为未考虑数据关联情况下基于蚂蚁自调整觅食行为的多细胞跟踪系统。Figure 1 shows a multicellular tracking system based on ants' self-adjusting foraging behavior without considering data association.

图2为序列1的3D跟踪结果。Figure 2 shows the 3D tracking results of sequence 1.

图3为序列2的3D跟踪结果。Figure 3 shows the 3D tracking results of sequence 2.

图4为限定蚁群觅食范围演化过程。Figure 4 shows the evolution process of the limited ant colony foraging range.

图5为迭代过程中高斯蚁群重采样演化过程。Figure 5 shows the evolution process of Gaussian ant colony resampling in the iterative process.

具体实施方式Detailed ways

如图1所示，输入细胞图像序列后，根据前一帧蚁群及其信息素场的迭代结果对当前帧进行预测，形成高斯蚁群及高斯信息素场；在基于指数形式的蚂蚁工作模式下利用三种策略，即，蚁群觅食范围限定、蚁群重采样机制、蚁群觅食停止准则构建信息素场；然后计算蚁群的存在概率并融合相似蚁群，考虑存在概率大于阈值的蚁群及相应高斯信息素场进行细胞状态提取，实现多细胞的精确跟踪。As shown in Figure 1, after inputting the cell image sequence, the current frame is predicted according to the iterative results of the ant colony and its pheromone field of the previous frame to form a Gaussian ant colony and a Gaussian pheromone field; in the exponential-based ant working mode Next, three strategies are used, namely, the ant colony foraging range limitation, the ant colony resampling mechanism, and the ant colony foraging stop criterion to construct the pheromone field; then the existence probability of the ant colony is calculated and similar ant colonies are fused, considering that the existence probability is greater than the threshold The ant colony and the corresponding Gaussian pheromone field are used for cell state extraction to achieve accurate tracking of multiple cells.

所述蚁群及信息素场双预测步骤中预测方式如下：The prediction method in the double prediction step of the ant colony and the pheromone field is as follows:

1)设定在第k-1帧有Nk-1个细胞，与细胞对应的蚁群及信息素场也有Nk-1个，第ν(v＝1，...，Nk-1)组蚁群包含M个蚂蚁，状态表示为

Figure GDA0003200753810000051
服从均值为
Figure GDA0003200753810000052
协方差为
Figure GDA0003200753810000053
的高斯分布
Figure GDA0003200753810000054
其中l表示蚂蚁，xk-1为第k-1帧蚂蚁状态变量，
Figure GDA0003200753810000055
和
Figure GDA0003200753810000056
分别为第k-1帧第v组蚁群蚂蚁状态变量的均值及协方差。第k-1帧第ν组蚁群中蚂蚁l的状态
Figure GDA0003200753810000057
预测到第k帧为
Figure GDA0003200753810000058
其中F为状态转移矩阵，
Figure GDA0003200753810000059
表示第k帧第ν组蚁群中蚂蚁l的预测状态，服从均值为
Figure GDA00032007538100000510
协方差为
Figure GDA00032007538100000511
的高斯分布
Figure GDA0003200753810000061
xk|k-1表示预测到第k帧的蚂蚁状态变量，
Figure GDA0003200753810000062
其中“∑”表示求和运算，
Figure GDA0003200753810000063
T表示矩阵转置；1) It is assumed that there are N k-1 cells in the k-1th frame, and there are also N k-1 ant colonies and pheromone fields corresponding to the cells, and the νth (v=1,..., Nk-1 ) group ant colony contains M ants, and the state is expressed as
Figure GDA0003200753810000051
obey the mean
Figure GDA0003200753810000052
The covariance is
Figure GDA0003200753810000053
Gaussian distribution of
Figure GDA0003200753810000054
where l represents the ant, x k-1 is the ant state variable in the k-1th frame,
Figure GDA0003200753810000055
and
Figure GDA0003200753810000056
are the mean and covariance of the state variables of the ants in the vth group of ants in the k-1th frame, respectively. The state of ant l in the nth group ant colony at frame k-1
Figure GDA0003200753810000057
It is predicted that the kth frame is
Figure GDA0003200753810000058
where F is the state transition matrix,
Figure GDA0003200753810000059
Represents the predicted state of ant l in the νth group ant colony in the kth frame, obeying the mean of
Figure GDA00032007538100000510
The covariance is
Figure GDA00032007538100000511
Gaussian distribution of
Figure GDA0003200753810000061
x k|k-1 represents the state variable of the ant predicted to the kth frame,
Figure GDA0003200753810000062
where "∑" represents the summation operation,
Figure GDA0003200753810000063
T represents matrix transpose;

2)假定第k-1帧第ν组信息素场

Figure GDA0003200753810000064
符合均值为
Figure GDA0003200753810000065
协方差为
Figure GDA0003200753810000066
的高斯分布
Figure GDA0003200753810000067
则第v组蚁群信息素场预测到第k帧为
Figure GDA0003200753810000068
其中，
Figure GDA0003200753810000069
为第ν组第k帧预测信息素场，τk|k-1表示第k帧信息素变量；2) Assume that the νth group pheromone field of the k-1th frame
Figure GDA0003200753810000064
conforming to the mean
Figure GDA0003200753810000065
The covariance is
Figure GDA0003200753810000066
Gaussian distribution of
Figure GDA0003200753810000067
Then the vth group ant colony pheromone field predicts the kth frame as
Figure GDA0003200753810000068
in,
Figure GDA0003200753810000069
is the predicted pheromone field for the kth frame of the νth group, and τ k|k-1 represents the kth frame pheromone variable;

所述蚂蚁自调整觅食步骤具体方式如下：The specific methods of the ants self-adjusting foraging steps are as follows:

1)输入细胞图像序列，构建信息素场中的基于指数形式的蚂蚁工作模式。蚂蚁的觅食行为限定在规定范围内并根据概率选择邻域内像素进行搜索。假如第v组蚁群中的蚂蚁l处于像素(i′，j′)所在位置，考虑指数形式对变量的变化比较敏感，则该蚂蚁选择其可用邻域内某一像素(i，j)的概率为：1) Input the cell image sequence, and construct the ant working mode based on the exponential form in the pheromone field. The foraging behavior of ants is limited to a specified range and the pixels in the neighborhood are selected according to the probability to search. If the ant l in the vth group ant colony is located at the position of the pixel (i', j'), considering that the exponential form is more sensitive to the change of variables, the probability of the ant selecting a pixel (i, j) in its available neighborhood for:

Figure GDA00032007538100000610
Figure GDA00032007538100000610

其中

Figure GDA00032007538100000611
为第v组蚁群像素(i，j)上第t次迭代的信息素，ηi，j是像素(i，j)的启发式函数。α和β是信息素
Figure GDA00032007538100000612
和启发式函数ηi，j之间的调节参数，Ω(i′，j′)是像素(i′，j′)的可用邻域集合；Ω(i′，j′)是限定蚂蚁觅食范围与像素(i′，j′)邻域的交集。in
Figure GDA00032007538100000611
is the pheromone of the t-th iteration on the v-th group of ant colony pixels (i, j), and η i, j is the heuristic function of the pixel (i, j). Alpha and beta are pheromones
Figure GDA00032007538100000612
and the heuristic function η i, j , Ω(i', j') is the set of available neighborhoods for the pixel (i', j');Ω(i',j') is the limited ant foraging The intersection of the range and the neighborhood of the pixel (i', j').

启发式函数ηi，j定义为

Figure GDA00032007538100000613
其中ΔIi，j和ΔAi，j分别表示像素(i，j)邻域内的像素强度差分和平均值。λ是调节系数，决定ΔIi，j和ΔAi，j两个变量对启发式函数值的影响，定义为λ＝Imean/Imax，其中Imean和Imax分别表示当前帧像素的平均强度和最大强度。γ和κ都是调节系数保证启发式函数值在区间[0，1]之间变化。如果图像背景的启发式函数值大于前景的，则γ＝1，否则γ＝2。同样如果启发式函数值大于1，则κ＝1，否则，κ＝0。The heuristic function η i,j is defined as
Figure GDA00032007538100000613
where ΔI i,j and ΔA i,j represent the pixel intensity difference and average value in the neighborhood of pixel (i,j), respectively. λ is the adjustment coefficient, which determines the influence of the two variables ΔI i,j and ΔA i,j on the heuristic function value, which is defined as λ=I mean /I max , where I mean and I max represent the average intensity of the current frame pixel respectively and maximum strength. Both γ and κ are adjustment coefficients to ensure that the heuristic function value varies between the interval [0, 1]. If the value of the heuristic function for the background of the image is greater than that of the foreground, then γ=1, otherwise γ=2. Also if the heuristic function value is greater than 1, then κ=1, otherwise, κ=0.

2)当所有蚂蚁完成搜索后，对像素(i，j)上的信息素量进行更新

Figure GDA0003200753810000071
其中
Figure GDA0003200753810000072
为第y组蚁群第t次迭代在像素(i，j)上的信息素量，ρ(0＜ρ＜1)表示信息素残留系数，
Figure GDA0003200753810000073
为第t-1次迭代蚂蚁l在像素(i，j)上释放的信息素量；2) When all ants complete the search, update the amount of pheromone on the pixel (i, j)
Figure GDA0003200753810000071
in
Figure GDA0003200753810000072
is the amount of pheromone on the pixel (i, j) in the t-th iteration of the y-th ant colony, ρ(0<ρ<1) represents the pheromone residual coefficient,
Figure GDA0003200753810000073
is the amount of pheromone released by the ant l on the pixel (i, j) in the t-1th iteration;

3)当第ν组蚁群中所有蚂蚁完成第t次迭代后，对第ν组信息素场进行高斯拟合，得到第ν组高斯信息素场，信息素变量服从均值为

Figure GDA0003200753810000074
协方差为
Figure GDA0003200753810000075
的高斯分布
Figure GDA0003200753810000076
其中τ(ν)(t)为第t次迭代后第v组高斯信息素场，τ(t)表示信息素变量，
Figure GDA0003200753810000077
和
Figure GDA0003200753810000078
分别为第t次迭代后第ν组高斯信息素场信息素量的均值及协方差；3) After all the ants in the νth group ant colony complete the t-th iteration, perform Gaussian fitting on the νth group pheromone field to obtain the νth group Gaussian pheromone field, and the pheromone variables obey the mean value.
Figure GDA0003200753810000074
The covariance is
Figure GDA0003200753810000075
Gaussian distribution of
Figure GDA0003200753810000076
where τ (ν) (t) is the v-th Gaussian pheromone field after the t-th iteration, and τ(t) represents the pheromone variable,
Figure GDA0003200753810000077
and
Figure GDA0003200753810000078
are the mean and covariance of the pheromone amount of the νth group of Gaussian pheromone field after the t-th iteration;

4)计算第t次迭代后第ν组高斯信息素场和第t-1次迭代后第ν组高斯信息素场之间的KL距离Dτ(t)，如果Dτ(t)大于阈值ε，则对第t次迭代后第ν组蚁群进行高斯重采样，得到高斯蚁群

Figure GDA0003200753810000079
为第t+1次迭代第v组蚁群的初始分布，其中x(v，l)(t+1)表示第t+1次迭代第v组蚁群蚂蚁l的状态，而且x(v，j)(t+1)服从均值为
Figure GDA00032007538100000710
协方差为
Figure GDA00032007538100000711
的高斯分布，x(ν，l)(t+1)：
Figure GDA00032007538100000712
同时根据第t次迭代后第v组高斯信息素场重构第ν组蚁群在第t+1次迭代中的蚂蚁觅食范围；4) Calculate the KL distance D τ (t) between the ν-th Gaussian pheromone field after the t-th iteration and the ν-th Gaussian pheromone field after the t-1th iteration, if D τ (t) is greater than the threshold ε , then the Gaussian resampling is performed on the νth group ant colony after the t-th iteration, and the Gaussian ant colony is obtained.
Figure GDA0003200753810000079
is the initial distribution of the vth group ant colony at the t+1th iteration, where x (v, l) (t+1) represents the state of the vth group ant colony l at the t+1th iteration, and x (v, j) (t+1) obeys the mean
Figure GDA00032007538100000710
The covariance is
Figure GDA00032007538100000711
Gaussian distribution of , x (ν, l) (t+1):
Figure GDA00032007538100000712
At the same time, according to the Gaussian pheromone field of the vth group after the tth iteration, the ant foraging range of the νth group ant colony in the t+1th iteration is reconstructed;

5)继续上述步骤1)-4)，直至Dτ(t)小于阈值ε，达到迭代终止条件。5) Continue the above steps 1)-4) until D τ (t) is less than the threshold ε and the iteration termination condition is reached.

所述细胞状态估计步骤的具体方式如下：The specific manner of the cell state estimation step is as follows:

1)计算存在概率r(v)：当达到迭代终止条件，第v组蚁群中所有蚂蚁完成移动后，形成信息素场τ(v)，计算第v组蚁群的存在概率，

Figure GDA00032007538100000713
Figure GDA00032007538100000714
为第v组信息素场像素
Figure GDA00032007538100000715
上的信息素量，
Figure GDA00032007538100000717
为像素
Figure GDA00032007538100000716
上的启发式函数值，Γ(ν)为当前帧第ν组蚁群对应细胞轮廓内的像素集。1) Calculate the existence probability r (v) : when the iteration termination condition is reached, after all the ants in the vth group of ants have completed their movement, a pheromone field τ (v) is formed, and the existence probability of the vth group of ant colonies is calculated,
Figure GDA00032007538100000713
Figure GDA00032007538100000714
is the vth group of pheromone field pixels
Figure GDA00032007538100000715
The amount of pheromone on the
Figure GDA00032007538100000717
for pixels
Figure GDA00032007538100000716
On the heuristic function value, Γ (ν) is the pixel set in the contour of the corresponding cell of the νth group of ant colonies in the current frame.

2)当第ν组蚁群的存在概率大于预先设定的阈值(本发明中设为0.5)，则保留第v组蚁群，否则删除第ν组蚁群；2) when the existence probability of the νth group ant colony is greater than the preset threshold (set as 0.5 in the present invention), then keep the vth group ant colony, otherwise delete the νth group ant colony;

3)融合空间相似蚁群后，进行细胞状态估计。3) After fusion of spatially similar ant colonies, cell state estimation is performed.

本发明经过蚁群及信息素场双预测步骤、蚂蚁自调整觅食步骤及细胞状态估计步骤的多细胞跟踪结果如下所示。The multi-cell tracking results of the present invention through the double prediction steps of the ant colony and the pheromone field, the ant self-adjusting foraging step and the cell state estimation step are as follows.

图1为基于蚂蚁自调整觅食行为的多细胞跟踪系统。图2为序列1的3D跟踪结果，图3为序列1的3D跟踪结果，可看出存在细胞出现、消失和细胞近邻等情况，都得到了可靠跟踪。图4为限定蚁群觅食范围演化过程，可看出随着迭代次数的增加蚁群觅食范围向细胞轮廓逼近。图5为迭代过程中高斯蚁群重采样演化过程。Figure 1 shows a multicellular tracking system based on ants' self-adjusting foraging behavior. Figure 2 shows the 3D tracking results of sequence 1, and Figure 3 shows the 3D tracking results of sequence 1. It can be seen that there are situations such as cell appearance, disappearance, and cell neighbors, all of which have been reliably tracked. Figure 4 shows the evolution process of the limited foraging range of the ant colony. It can be seen that the foraging range of the ant colony approaches the cell outline with the increase of the number of iterations. Figure 5 shows the evolution process of Gaussian ant colony resampling in the iterative process.

本发明所设计的方法与基于信息素预测的蚁群多细胞跟踪算法，SMAL博士提出的粒子滤波器细胞跟踪方法及REZA教授提出的多贝努利滤波器及高斯混合PHD滤波器相比，精确度Precision(P),回波率Recall(R)和F1-测量都得到了提升，如表一和表二所示。Compared with the ant colony multi-cell tracking algorithm based on pheromone prediction, the particle filter cell tracking method proposed by Dr. SMAL, and the multi-Bernoulli filter and Gaussian mixture PHD filter proposed by REZA, the method designed in the present invention is more accurate. Degree Precision(P), Echo Rate Recall(R) and F1-measurement have all been improved, as shown in Tables 1 and 2.

表一 不同算法跟踪性能比较(序列1)Table 1 Tracking performance comparison of different algorithms (sequence 1)

Figure GDA0003200753810000081
Figure GDA0003200753810000081

表二 不同算法跟踪性能比较(序列2)Table 2 Tracking performance comparison of different algorithms (sequence 2)

Figure GDA0003200753810000082
Figure GDA0003200753810000082

综上所述，本发明技术方案可解决在数目时变、变形及运动特性各异时的多细胞跟踪问题。对细胞近距离交互、细胞进入或离开视图和细胞运动速度方向时变等情形，利用蚂蚁自调整觅食行为考虑三种策略，即，限定蚁群觅食范围、蚁群重采样机制、蚁群觅食停止准则构建信息素场，实现复杂情形下多细胞的精确跟踪。To sum up, the technical solution of the present invention can solve the problem of multi-cell tracking when the number is time-varying, the deformation and the motion characteristics are different. For the case of close cell interaction, cell entering or leaving the view, and time-varying direction of cell movement speed, three strategies are considered by using ants' self-adjusting foraging behavior, namely, limiting the foraging range of ant colonies, ant colony resampling mechanism, ant colony The foraging stop criterion constructs a pheromone field, enabling accurate tracking of multiple cells in complex situations.

Claims (5)

1. A multi-cell tracking method based on ant self-regulation foraging behavior is characterized by comprising the following steps:
an ant colony and pheromone field double-prediction step, wherein an original image is input, and based on the ant colony and the result pheromone field of the previous frame, the ant colony and the pheromone field of the current frame are predicted by utilizing a Gaussian model;
the ants self-adjust foraging step, which utilizes three strategies under an exponential-form-based ant working mode, namely limiting an ant colony foraging range, an ant colony resampling mechanism and an ant colony foraging stopping criterion to construct an pheromone field, and realizes deformation, number change, uncertain motion state and adjacent cell tracking;
a cell state estimation step, namely calculating the existence probability of each sub-ant colony based on the result pheromone field and a heuristic function, deleting the ant colony of which the existence probability is smaller than a threshold value, fusing similar ant colonies and considering the ant colony of which the existence probability is larger than the threshold value to carry out multi-cell state estimation;
wherein, the ants self-adjust foraging steps are as follows:
1) inputting a cell image sequence, and constructing an exponential-form-based ant working mode in an pheromone field; the foraging behavior of ants is limited in a specified range, and pixels in the neighborhood are selected according to the probability for searching; if an ant/in the v-th ant group is in a position of a pixel (i ', j'), considering that the exponential form is sensitive to the variation of the variable, the probability that the ant selects a certain pixel (i, j) in its available neighborhood is:
Figure FDA0003200753800000011
wherein
Figure FDA0003200753800000012
For the pheromone, η, of the t-th iteration on the v-th ant colony pixel (i, j)i,jIs a heuristic function of the pixel (i, j); alpha and beta are pheromones
Figure FDA0003200753800000013
And a heuristic function ηi,jQ (i ', j') is the set of available neighborhoods for pixel (i ', j'); Ω (i ', j') is the intersection of the neighborhood of the pixel (i ', j') and the range of foraging defined by the ant;
heuristic function etai,jIs defined as
Figure FDA0003200753800000014
Wherein Δ Ii,jAnd Δ Ai,jRespectively representing the pixel intensity difference and the mean value in the neighborhood of the pixel (i, j); λ is the adjustment coefficient, determining Δ Ii,jAnd Δ Ai,jThe influence of two variables on the heuristic function value is defined as λ ═ Imean/ImaxIn which ImeanAnd ImaxRespectively representing the average intensity and the maximum intensity of the current frame pixel; gamma and kappa are both regulating coefficients to ensure that the heuristic function value is in the interval [0, 1%]Change in between; if the heuristic function value of the image background is larger than the foreground, the gamma is 1, otherwise, the gamma is 2; if the heuristic function value is larger than 1, k is equal to 1, otherwise k is equal to 0;
2) when all ants complete the search, the amount of the pheromone on pixel (i, j) is updated
Figure FDA0003200753800000021
Wherein
Figure FDA0003200753800000022
The amount of pheromone on the pixel (i, j) for the tth iteration of the vth group of ant colony, rho (0 < rho < 1) represents the pheromone residual coefficient,
Figure FDA0003200753800000023
the amount of pheromone released by ant l on pixel (i, j) for the t-1 st iteration;
3) after all ants in the v-th group of ant colony complete the t-th iteration, Gaussian fitting is carried out on the v-th group of pheromone field to obtain a v-th group of Gaussian pheromone field, and pheromone variables obey the mean value of
Figure FDA0003200753800000024
Covariance of
Figure FDA0003200753800000025
Is a Gaussian distribution of(ν)(t)≈N(τ(t)；
Figure FDA0003200753800000026
Wherein tau is(ν)(t) is the ν -th group of Gaussian pheromone fields after the tth iteration, τ (t) represents pheromone variables,
Figure FDA0003200753800000027
and
Figure FDA0003200753800000028
respectively mean value and covariance of the v group Gaussian pheromone field pheromone quantity after the t iteration;
4) calculating KL distance D between the v group of Gaussian pheromone fields after the t iteration and the v group of Gaussian pheromone fields after the t-1 iterationτ(t) if Dτ(t) if the t is larger than the threshold epsilon, Gaussian resampling is carried out on the v group ant colony after the t iteration, and a Gaussian ant colony is obtained
Figure FDA0003200753800000029
Initial distribution of the ν th ant colony for the t +1 th iteration, where x(ν,l)(t +1) denotes the status of the v-th group ant l for the t +1 th iteration, and x(ν,l)(t +1) obeys an average of
Figure FDA00032007538000000210
Covariance of
Figure FDA00032007538000000211
Gaussian distribution of (x)(ν,l)(t+1):
Figure FDA00032007538000000212
Reconstructing the ant foraging range of the ν -th group of ant colony in the (t +1) th iteration according to the ν -th group of Gaussian pheromone field after the t-th iteration;
5) continuing the steps 1) to 4) until Dτ(t) is less than a threshold epsilon and an iteration termination condition is reached.
2. The ant-based multicellular tracking method for self-adjusting foraging behavior of ants according to claim 1, wherein the ant colony and pheromone field double prediction steps are specifically as follows:
1) setting N in the k-1 th framek-1The individual cells, the ant colony and pheromone field corresponding to the cells also have Nk-1V (1., N) thk-1) The ant group comprises M ants, and the state is expressed as
Figure FDA00032007538000000213
Obey mean value of
Figure FDA00032007538000000214
Covariance of
Figure FDA0003200753800000031
Gaussian distribution of
Figure FDA0003200753800000032
Wherein l represents an ant, xk-1Is the ant state variable of the (k-1) th frame,
Figure FDA0003200753800000033
and
Figure FDA0003200753800000034
respectively mean value and covariance of the v group ant state variables of the k-1 frame; state of ants l in v-th group ant colony of frame k-1
Figure FDA0003200753800000035
Predict the k frame as
Figure FDA0003200753800000036
Wherein F is a state transition matrix and wherein,
Figure FDA0003200753800000037
representing the predicted state of ant l in the v group of ant colony of the k frame, subject to the mean value of
Figure FDA0003200753800000038
Covariance of
Figure FDA0003200753800000039
Gaussian distribution of
Figure FDA00032007538000000310
xk|k-1Indicating that the ant state variable of the k-th frame is predicted,
Figure FDA00032007538000000311
where "Σ" denotes a summation operation,
Figure FDA00032007538000000312
t represents matrix transposition;
2) suppose that the v group pheromone field of the k-1 frame
Figure FDA00032007538000000313
In agreement with an average value of
Figure FDA00032007538000000314
Covariance of
Figure FDA00032007538000000315
Gaussian distribution of
Figure FDA00032007538000000316
Then the v-th group pheromone field predicts the k-th frame as
Figure FDA00032007538000000317
Wherein,
Figure FDA00032007538000000318
predicting the pheromone field, tau, for the kth frame of the set vk|k-1Representing the k-th frame pheromone variable.
3. The ant-based multicellular tracking method for self-regulating foraging behavior of claim 1, wherein the cell state estimation step is implemented in a specific manner as follows:
1) calculating the existence probability r(ν): when the iteration termination condition is reached and all ants in the v-th group of ant colony finish moving, an pheromone field tau is formed(ν)Calculating the existence probability of the v group ant colony
Figure FDA00032007538000000319
Figure FDA00032007538000000320
For a v-th group of pixels of an information element field
Figure FDA00032007538000000321
The amount of the pheromone on the surface,
Figure FDA00032007538000000322
is a pixel
Figure FDA00032007538000000323
Value of the heuristic function of(ν)A pixel set in the cell outline corresponding to the v-th group of ant colony of the current frame;
2) when the existence probability of the v-th ant colony is greater than a preset threshold value, the v-th ant colony is reserved, otherwise, the v-th ant colony is deleted;
3) and after fusing the space similar ant colony, performing cell state estimation.
4. The ant-based multicellular tracking method of self-regulating foraging behavior of claim 3, wherein: and setting the existence probability of the ν th ant colony to be greater than a preset threshold value to be 0.5.
5. A multi-cell tracking system, comprising: comprising a memory and a processor, the memory storing a computer program, characterized in that; the processor, when executing the computer program, realizes the method steps of any of claims 1-4.
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