CN100545640C - A Method for Automatic Tracking of Cells in Video Microscopic Image - Google Patents

Abstract

The invention relates to a method for automatically tracking cells in a video microscopic image. The existing cell tracking methods have a low degree of automation and cannot adapt to the complexity and variability of cell movement patterns and multi-cell movement tracking. The steps of the invention include: enhancing the acquired cell movement video microscopic image frame by frame; extracting target cells from the enhanced cell movement images; establishing a cell movement dynamics model; tracking the moving target cells. Based on the analysis of cell motion characteristics and image noise and interference features, the present invention adopts dynamic system modeling and stochastic modeling methods, and uses recursive Bayesian filtering and data association technology to track cell motion trajectories, with a high degree of automation , Strong processing ability.

Description

A Method for Automatic Tracking of Cells in Video Microscopic Image

technical field

The invention belongs to the field of cell biology and biopharmaceuticals, and relates to a method for automatic tracking of cells in video microscopic images.

Background technique

Cell tracking refers to the qualitative or quantitative analysis of the trajectory, speed, color, shape and other attributes of specific cells within the observation time. It has very important research significance and practical value in biology, pharmacology and pathology.

At present, the domestic cell tracking method is mainly manual timing detection and recording with the aid of microscopic equipment, and its degree of automation is relatively low. On the one hand, it requires the staff to work hard and has high labor intensity; on the other hand, due to the complexity and variability of cell movement (such as cell division, combination, aggregation, crossover) and the noise and interference of the video image itself, It makes the manual observation process more difficult and has a higher error rate.

In recent years, foreign research institutes have achieved some research results in automatic cell tracking. With the help of image analysis software, a number of automatic cell tracking systems (such as University of Virginia, University of Aberdeen and European Molecular Biology Laboratory, etc.) have been developed. Culturally immature. Although these devices can calculate the position of cells on the image through image processing and analysis software, it is difficult to deal with complex phenomena such as cell division and combination, cell aggregation and separation of cell groups, and the intersection of multi-cell movement trajectories.

Contents of the invention

The purpose of the present invention is to aim at the deficiency of existing cell tracking methods, and provide a method for cell tracking of video microscopic images with high degree of automation and strong processing capacity for research in the fields of cell biology and biopharmaceuticals.

The present invention comprises the following steps: 1. Obtain real-time cell motion images through a phase contrast microscope, and enhance the acquired cell motion video microscopic images frame by frame; 2. Extract target cells from the enhanced cell motion images; 3. Establish a dynamic model of cell movement; 4. Track the moving target cells.

The enhancement processing of the video microscopic image in step 1 adopts the generalized fuzzy enhancement processing method, and the specific steps are as follows:

1) Initialize, input the image f to be processed, and set the initial value of the number of iterations as r=1;

2) Use the median filter for smoothing, take each pixel f(i, j) of the image f as the center of the window (a unit that can cover a certain image), and take the average gray value of the pixel of the image covered by the window as new gray value f _ij of pixel f(i, j);

3) Carry out the rth iteration of the new gray value f _ij to determine the fuzzy feature plane {μ _ij (r)} of the image after median filtering;

4) Perform the following nonlinear transformation on μ _ij (r), and the transformation result is recorded as μ′ _ij (r);

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 2</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0.5</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

5) Perform inverse transformation on μ′ _ij (r) to obtain a new grayscale image {f′ _ij };

6) Gray scale transformation, set appropriate f _min ^e , f _max ^e , and calculate the image gray scale {f _ij ^e } after generalized fuzzy enhancement;

7) Compare the image quality evaluation indicators of the rth and r-1th enhanced images, if _σw (r) is less than _σw (r-1), then let ${\mathrm{\&mu;}}_{\mathrm{ij}}^{\&prime;}\left(r\right)\stackrel{\mathrm{\&Delta;}}{=}{\mathrm{\&mu;}}_{\mathrm{ij}}\left(r\right),$ $r+1\&DoubleRightArrow;r,$ And return to 4) perform iterative calculation on μ _ij (r); otherwise, output the image enhanced for the r-1th time.

The computational complexity of the above algorithm can be analyzed as follows: For an image with m×n pixels, the computational complexity of the generalized blur enhancement algorithm is O(m×n).

The method for extracting target cells in step 2 adopts the active contour model method (Snake method), and the specific implementation includes the following steps:

1) Construct an energy model

Set the curve v(s)=[x(s) y(s)], s∈[0,1], define the total energy on it as:

E _total (v(s))＝∫ _s (E _int (v(s))+E _image (v(s))+E _con (v(s)))ds (1)

Where: E _int (v(s))＝(α(s)|v _s (s)| ² +β(s)|v _ss (s)| ² ) (2)

E _image (v(s))＝w _line E _line (v(s))+w _edge E _edge (v(s))+w _term E _term (v(s)) (3)

E _con (v(s))＝k(x ₁ -x ₂ ) ² (4)

E _int (v(s)) is the internal energy, which expresses the force that drives the curve smoother, where the first-order term expresses the pulling force that makes the distance between adjacent points smaller, and the second-order term expresses the rigid force against bending; α( s) and β(s) represent their respective weights; E _image (v(s)) is the image energy, which is the line energy obtained from the image to guide the snake to advance towards the low gray level or high gray level position E _line =I(x , y), the edge energy is used ${\mathrm{E.}}_{\mathrm{edge}}=-|\&dtri;I\left(v\left(\mathrm{the\; s}\right)\right)|$ and the weighted sum of the three energy items of the energy E _term of the impact of the end point and corner of the line in the image on the direction of the contour line; w _line , w _edge and w _term represent the weight of each component of the image energy; E _con (v(s) ) represents the elastic force that attracts the contour line to the image position, and x ₁ and x ₂ represent the designated points of the contour line and image position, respectively. If the external energy is defined as

E _ext (v(s))＝E _image (v(s))+E _con (v(s)) (5)

Then the total energy is

E _total (v(s))＝∫ _s (E _int (v(s))+E _ext (v(s)))ds (6)

2) Use the variation method to minimize the total energy, so that the contour line satisfies

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ss</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

3) The position of the cell target on the image is determined by the center position of the area surrounded by the curve, and this position is used as the position measurement of the cell image in the current frame.

Establishing a cell movement dynamics model in step 3 includes establishing a target movement model and a measurement model, wherein the target movement model is

x(k+1)＝F(k)x(k)+G(k)u(k)+v(k) (8)

The measurement model is

z(k)=H(k)x(k)+w(k) (9)

x(k) represents the motion state (position, velocity) of the target cell at time k, z(k) represents the image measurement at time k, and F(k), G(k) and H(k) represent the The state transition matrix, control input matrix, and measurement matrix, v(k) and w(k), describe random system noise and measurement noise, respectively.

In the tracking method of moving target cells in step 4, the recursive Bayesian filter method is used to update each target, and the current state and estimation accuracy of each target are obtained. Multi-cell tracking, cell division, and cell aggregation are processed through data association.

Both the recursive Bayesian filtering method and the joint probability data association method adopt mature existing technologies. For example, the recursive Bayesian filtering method can use methods such as α-β filtering, Kalman filtering, and PF filtering, and the data association adopts the joint probability data association method (by presented by Bar Shalom Y).

According to the characteristics of strong noise and disturbance and poor image contrast of video microscopic images, the present invention adopts the generalized fuzzy enhancement method composed of median filtering, fuzzy enhancement, gray scale transformation and image quality evaluation links to process the original image data frame by frame. Processing can greatly improve the image processing effect. Compared with common image enhancement methods, the proposed generalized fuzzy enhancement algorithm has better performance in dealing with weak contrast and strong noise images.

The invention starts from the acquired original video microscopic image, uses image processing and analysis methods to improve image quality, extract cell outline and determine cell position, thereby obtaining time-series observation data. On the basis of analyzing the characteristics of cell movement and the characteristics of noise and interference in the image, the dynamic system modeling and stochastic modeling methods are used to establish the model of the cell movement system, and the trajectory of the cell is analyzed by recursive Bayesian filtering and data association technology. Automatic tracking, while giving the tracking results of complex movement of cells. The invention has complete system and strong practicability.

Detailed ways

The method for automatically tracking cells in a video microscopic image comprises the following steps: 1. Obtain a real-time cell motion image through a phase contrast microscope, and enhance the acquired cell motion video microscopic image frame by frame; 2. From the enhanced cell motion image 3. Establish a dynamic model of cell movement; 4. Track the moving target cells.

The enhancement processing of the video microscopic image in step 1 adopts the generalized fuzzy enhancement processing method, and the specific steps are as follows:

(1) In order to weaken the granular noise in the image, in general, the neighborhood average can be used to reduce the noise in the spatial domain. In the frequency domain, because the noise spectrum is mostly in the high frequency band, various forms of low-pass filtering methods can be used to reduce noise. In order to avoid image edge blurring and remove impulse noise and so-called "salt-and-pepper" noise (Salt-and-pepper noise), a median filter is used for smoothing;

(2) Use the following transformation method for image enhancement

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; )</span>}^{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}$

Among them, F _c is the fuzzy characteristic parameter, f _ij , f _max , and f _min respectively represent the gray value of pixel (i, j) in the image, the maximum gray value and the minimum gray value of the image, μ _ij represents the pixel ( i, j) Fuzzy membership degree. The iterative operation is used to enhance the image fuzzy feature plane {μ _ij } to obtain a new fuzzy feature plane {μ′ _ij }, and on this basis, the following inverse transformation is performed to obtain the gray value of the image after blur enhancement:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; )</span>$

(3) Perform the following grayscale transformation on the image after blur enhancement

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}$

In the formula, f _ij ^e is the gray value of the image after gray scale transformation t( ), f _min ^e and f _max ^e are the maximum and minimum values of the gray scale of the image after the set gray scale transformation respectively, and f′ _min , f′ _max are the maximum and minimum values of the grayscale of the blur-enhanced image respectively, and $f_{\min }^{\&prime;}\&Greater\; Equal;f_{\min }^e,$ $f_{\max }^{\&prime;}\&le;f_{\max }^e.$

(4) Weighting the standard deviation of its gray histogram by using the image gray level, the following image quality evaluation index is obtained

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Delta;f</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\sqrt{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}}$

Where σ _w is the weighted standard deviation of the grayscale histogram of the image, _pj is the percentage of the number of pixels of the jth grayscale level in the total pixels N of the image, p is the average value of _pj , and Δf is the grayscale of the image scope.

(5) Repeat steps (2)-(4) until the image quality evaluation index σ _w no longer decreases.

The method of extracting target cells in step 2 adopts the active contour line model method (Snake method), which is a top-down mechanism for locating image features, first setting an initial contour line (“snake”), and then passing The constraint force acting on the "snake point" pushes the contour line to the direction of the image feature, and finally locks the target structure by minimizing the integral measurement of the overall energy of the dynamic contour line. The specific implementation includes the following steps:

(1) Construction of energy model

Let the curve v(s)=[x(s) y(s)], s∈[0,1], then the total energy defined on it can be expressed as:

E _total (v(s))＝∫ _s (E _int (v(s))+E _image (v(s))+E _con (v(s)))ds (1)

Where: E _int (v(s))＝(α(s)|v(s)| ² +β(s)|v _ss (s)| ² ) (2)

E _image (v(s))＝w _line E _line (v(s))+w _edge E _edge (v(s))+w _term E _term (v(s)) (3)

E _con (v(s))＝k(x ₁ -x ₂ ) ² (4)

The internal energy E _int (v(s)) expresses the force that drives the curve smoother, where the first-order term expresses the pulling force that makes the distance between adjacent points smaller, and the second-order term expresses the rigid force against bending, α(s) and β(s) represent the respective weights. The image energy E _image (v(s)) is the weighted sum of three energy items obtained from the image: the line energy that guides the snake towards a low-gray or high-gray position, E _line =I(x,y); edge For energy ${\mathrm{E.}}_{\mathrm{edge}}=-|\&dtri;I\left(v\left(\mathrm{the\; s}\right)\right)|$ Indicates that the contour line is attracted to the edge point of the image with a high gradient modulus; E _term represents the influence of the end point and corner of the line in the image on the direction of the contour line. w _line , _wedge and w _term represent the weight of each component of image energy. E _con (v(s)) expresses the elastic force that attracts the contour line to a specified position, and x ₁ and x ₂ represent the specified point of the contour line and image position, respectively. Ruoji

E _ext (v(s))＝E _image (v(s))+E _con (v(s)) (5)

then there is

E _total (v(s))＝∫ _s (E _int (v(s))+E _ext (v(s)))ds (6)

(2) Energy minimization calculation based on variational method

The final position of the contour line can be obtained by a variational method. Replace the integral term in (6) with F(s, vs, v _ss ), then the derived curve equation should satisfy the following Euler-Lager Lange equation:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ss</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

(3) On the results processed by the active contour model method, the position of the cell target on the image can be determined by calculating the center position of the area surrounded by the curve. The position can be measured as the position of a certain cell in the current frame image.

Due to the randomness of cell movement, stochastic modeling is used to establish the dynamic model of cell movement in step 3 of its movement description, including the establishment of target movement model and measurement model, where the target movement model is

x(k+1)＝F(k)x(k)+G(k)u(k)+v(k) (8)

The measurement model is

z(k)＝H(k)x(k)+w(k)

x(k) represents the motion state (position, velocity) of the target cell at time k, z(k) represents the image measurement at time k, and F(k), G(k) and H(k) represent the The state transition matrix, control input matrix, and measurement matrix, v(k) and w(k), describe random system noise and measurement noise, respectively.

In the tracking method of moving target cells in step 4, the recursive Bayesian filter method is used to update each target, and the current state and estimation accuracy of each target are obtained. Multi-cell tracking, cell division, and cell aggregation are processed through data association.

There are often multiple cells on the same frame of image, the movement of these cells is irregular, and there may be biological phenomena such as cell division and merger. Due to the performance of image acquisition equipment and the interference of the actual environment, the level of noise and clutter in the image is relatively high. These factors make image-based cell tracking must solve a key technical problem: data association, that is, to correctly judge the correlation between multiple measurement information and multiple tracked target tracks. Once the uncertainty of the measurement source is eliminated, the multi-target tracking problem can be transformed into multiple single-target tracking problems for solution. The clutter can be dealt with by tracking gate technology and stochastic modeling method, and the phenomenon of cell division and merging can be equivalent to the generation and merging of target tracks.

JPDA (Joint Probabilistic Data Association) is a suboptimal algorithm for solving data association problems. When tracking multiple targets approaching in the measurement space, the measurement may fall in the tracking gates of several targets at the same time, and the targets that these tracking gates intersect form a "cluster", and the number of targets in the cluster is n _t , The number n _m of measurements falling into these target tracking gates will be aggregated using a binary associative logic matrix $\mathrm{\&Omega;}={\left[{\mathrm{\&Omega;}}_{\mathrm{ij}}\right]}_{{\mathrm{no}}_m\&times;({\mathrm{no}}_i+1)}$ express. Ω _ij =1, which means that the i-th measurement may originate from the j-th target (j=0 means that the measurement is clutter); otherwise, Ω _ij =0 means that the i-th measurement cannot possibly originate from the j-th target. A possible pairing event between a measurement and a target that satisfies the following three constraints is called a feasible event χ (feasible event):

Each target produces at most one measurement;

Each measurement originates from at most one target;

Candidate measurements that fall within a target's tracking gate originate either from that target, from clutter, or from other targets.

表示可行事件χ中杂波个数。在源自目标的测量满足正态分布，杂波满足均匀分布，杂波个数满足泊松分布的前提下，得可行事件χ发生的后验概率为Feasible events are represented by a binary associative logic matrix Φ. According to the constraints of feasible events, the sum of elements in each row of Φ is equal to 1, and the sum of elements in each column is equal to 1 or 0 (except column 0). Feasible events can be regarded as partial combinations selected according to three constraints in all mathematical combinations formed by the measurement set and the undetermined target set. Find the posterior probability of each feasible event, and add the posterior probability of all Φ _ij = 1 feasible events, that is, the posterior probability that the i-th measurement belongs to the j-th target, and use it to find the measurement update The weight of this goal. remember ${\mathrm{\&tau;}}_i\left(\mathrm{\&chi;}\right)=\underset{j=1}{\overset{{\mathrm{no}}_t}{\mathrm{\&Sigma;}}}{\mathrm{\&Phi;}}_{\mathrm{ij}}$ Denotes the indicator function of the i-th measurement in the feasible event χ, ${\mathrm{\&delta;}}_i\left(\mathrm{\&chi;}\right)=\underset{i=1}{\overset{{\mathrm{no}}_t}{\mathrm{\&Sigma;}}}{\mathrm{\&Phi;}}_{\mathrm{ij}}$ represents the index function of the jth objective in the feasible event χ,

Indicates the number of clutter in the feasible event χ. Under the premise that the measurement from the target satisfies the normal distribution, the clutter satisfies the uniform distribution, and the number of clutter satisfies the Poisson distribution, the posterior probability of the occurrence of the feasible event χ is given as

Among them, the first multiplication indicates the probability that the measurement belongs to the normal distribution of the actual target, the second multiplication indicates the probability that all targets are detected, and the third multiplication indicates the probability that no target is detected, and c is the normalization factor. The posterior probability that the i-th measurement originates from the j-th target is

${\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; \&chi;</span>}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; \&Phi;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&chi;</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

The posterior probability that the jth target did not produce any measurement is

${\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

The fused measure is obtained by weighting all valid measures:

${\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Update each target according to the recursive Bayesian filter method (such as α-β filter, Kalman filter, PF filter, etc.), and obtain the current state (estimator) and estimation accuracy (target state covariance matrix) of each target.

Claims (1)

1, a kind of video microscopic image cell automatic tracking method, it is characterized in that the method comprises the following steps: (1) obtain real-time cell motion image by phase contrast microscope, the cell motion video microscopic image of acquisition is carried out frame-by-frame enhanced processing; 2) Extracting target cells from the enhanced cell motion image; (3) Establishing a cell motion dynamics model; (4) Tracking moving target cells; The enhanced processing of the video microscopic image in step (1) adopts a generalized fuzzy enhanced processing method, which specifically includes the following steps: ①Initialization, input the image f to be processed, and set the initial value of the number of iterations to r=1; ②Adopt the median filter for smoothing, take each pixel f(i, j) of the image f as the center of the window, and use the average gray value of the pixels of the image covered by the window as the new gray value of f(i, j) degree value f _ij ; ③The new gray value f _ij of each pixel is image enhanced according to the following transformation method ${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; )</span>}^{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}$ Among them, F _c is the fuzzy characteristic parameter, f _ij , f _max , and f _min respectively represent the gray value of pixel f(i, j) in the image, the maximum gray value and the minimum gray value of the image, and μ _ij represents the pixel f(i, j) fuzzy degree of membership; All new gray values f _ij are iterated for the rth time to determine the fuzzy feature plane {μ _ij (r)} of the image after median filtering; ④ Perform the following nonlinear transformation on μ _ij (r), and the transformation result is recorded as μ′ _ij (r); ${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 2</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0.5</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ ⑤ Perform inverse transformation on μ′ _ij (r) to obtain a new grayscale image {f′ _ij }; ⑥ Perform the following grayscale transformation on the image after blur enhancement ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ In the formula, f _ij ^e is the gray value of the image after gray scale transformation t( ), f _min ^e and f _max ^e are the maximum and minimum values of the gray scale of the image after the set gray scale transformation respectively, and f′ _min , f′ _max are the maximum and minimum values of the grayscale of the blur-enhanced image respectively, and $f_{\min }^{\&prime;}\&Greater\; Equal;f_{\min }^e,$ $f_{\max }^{\&prime;}\&le;f_{\max }^e;$ ⑦Comparing the image quality evaluation index of the rth enhanced image with the r-1th enhanced image, if σ _w (r) is less than σ _w (r-1), then let ${\mathrm{\&mu;}}_{\mathrm{ij}}^{\&prime;}\left(r\right)\stackrel{\mathrm{\&Delta;}}{=}{\mathrm{\&mu;}}_{\mathrm{ij}}\left(r\right),$ $r+1\&DoubleRightArrow;r,$ And return ④ to iteratively calculate μ _ij (r); otherwise, output the image enhanced for the r-1th time; The image quality evaluation index is weighted by the standard deviation of its gray histogram using the image grayscale, and the following image quality evaluation index is obtained ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\sqrt{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}}$ Where σ _w is the weighted standard deviation of the grayscale histogram of the image, _pj is the percentage of the number of pixels of the jth grayscale level in the total pixels N of the image, p is the average value of _pj , and Δf is the grayscale range of the image; The method for extracting target cells in step (2) adopts the active contour line model method, and the specific implementation includes the following steps: ①Construct energy model Set the curve v(s)=[x(s) y(s)], s∈[0,1], define the total energy on it as: E _total (v(s))＝∫ _s (E _int (v(s))+E _image (v(s))+E _con (v(s)))ds (3) in: E _int (v(s))＝(α(s)|v _s (s)| ² +β(s)|v _ss (s)| ² ) (4) E _image (v(s))＝w _line E _line (v(s))+w _edge E _edge (v(s))+w _term E _term (v(s)) (5) E _con (v(s))＝k(x ₁ -x ₂ ) ² (6) E _int (v(s)) is the internal energy, which expresses the force that drives the curve smoother, where the first-order term expresses the pulling force that makes the distance between adjacent points smaller, and the second-order term expresses the rigid force against bending; α( s) and β(s) represent their respective weights; E _image (v(s)) is the image energy, which is the line energy obtained from the image to guide the snake to advance towards the low gray level or high gray level position E _line =I(x , y), edge energy ${\mathrm{E.}}_{\mathrm{edge}}=-|\&dtri;I\left(v\left(\mathrm{the\; s}\right)\right)|$ and the weighted sum of the three energy items of the energy E _term of the impact of the end point and corner of the line in the image on the direction of the contour line; w _line , w _edge and w _term represent the weight of each component of the image energy; E _con (v(s) ) represents the elastic force that attracts the contour line to the image position, and x ₁ and x ₂ represent the designated points of the contour line and image position, respectively; ② Use the variational method to minimize the total energy, so that the contour line satisfies ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ss</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ ③ The position of the cell target on the image is determined by the center position of the area surrounded by the curve, and this position is used as the position measurement of the cell image in the current frame; Establishing the cell movement dynamics model in step (3) includes establishing a target movement model and a measurement model, wherein the target movement model is x(k+1)＝F(k)x(k)+G(k)u(k)+v(k) (8) The measurement model is z(k)=H(k)x(k)+w(k) x(k) represents the movement state of the target cell at time k, z(k) represents the image measurement at time k, F(k), G(k) and H(k) represent the state transition matrix, control The input matrix and the measurement matrix, v(k) and w(k) describe the random system noise and measurement noise, respectively; The tracking method of moving target cells in step (4) adopts the recursive Bayesian filtering method to update each target, obtains the current state and estimation accuracy of each target, and processes multi-cell tracking, cell division, and cell aggregation through data association.