A method for axial positioning error suppression in three-dimensional microscopic trajectory tracking

Abstract

The present invention discloses a method for suppressing axial positioning errors in three-dimensional microscopic trajectory tracking. The present invention relates to the technical field of particle positioning error suppression, and in particular to a method for suppressing axial positioning errors in three-dimensional microscopic trajectory tracking. The method comprises the following steps: obtaining the three-dimensional motion trajectory of the particle; performing Gaussian fitting in three orthogonal motion directions; performing axial positioning error suppression by Fourier transform high-order filtering; performing axial positioning error suppression based on the Winsorizing method; performing axial positioning error suppression by Gaussian distribution statistical parameters; and obtaining the three-dimensional motion trajectory of the particle target with the same degree of random jitter in the horizontal and axial directions. The present invention solves the problem that in the process of three-dimensional tracking of the particle, the axial positioning accuracy is different from that in the horizontal direction due to the limitation of the characterization method, thereby causing the three-dimensional motion trajectory of the particle to be distorted. It is particularly suitable for high signal-to-noise ratio systems. It is suitable for a variety of three-dimensional particle tracking technologies based on defocus imaging.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of microparticle positioning error suppression, and particularly relates to a method for axial positioning error suppression in three-dimensional microscopic trajectory tracking. BACKGROUND

[0002] With the continuous expansion of the application range of microorganisms and drug particles in the fields of medical treatment, industrial production, etc. and the rapid development of related scientific research technologies, people's microscopic characterization of microparticles, microbubbles or microorganisms is no longer limited to two-dimensional level. Three-dimensional particle tracking analysis based on microscopic imaging is gradually becoming an important real-time microscopic characterization method.

[0003] The commercially available three-dimensional particle tracking analysis technologies on the market include: fluorescence microscope based on out-of-focus imaging, digital holographic microscope method, total internal reflection microscope method, etc. These technologies mainly rely on two-dimensional optical imaging sensor planes (such as CMOS or CCD sensors of scientific research digital cameras, photomultiplier tube arrays, etc.) to obtain the three-dimensional real-time motion trajectory of the target sample, and usually need to use different imaging and positioning principles in the axial positioning than in the horizontal direction, which further leads to the inconsistency of the axial and horizontal positioning accuracy. This inconsistency of positioning accuracy not only leads to trajectory distortion, but also may introduce significant differences in the axial and horizontal direction data analysis of the trajectory, for example, the analysis of Mean Square Displacement (MSD) may be affected. Especially in the conditions of low exposure time, high frame rate and high signal-to-noise ratio, the differences and influences in the sample with relatively weak real signal will be more obvious. The commonly used trajectory smoothing processing method may also cause similar significant differences. At present, there is still a lack of effective solutions to solve the problem of trajectory distortion caused by the inconsistency of axial and horizontal positioning errors. SUMMARY

[0004] The application provides an axial positioning error suppression method in three-dimensional microscopic trajectory tracking. The method is a three-dimensional motion trajectory data optimization method based on statistical rules, utilizes isotropy of Brownian motion of particles and Gaussian distribution characteristics of instantaneous velocity, and combines a plurality of non-smooth trajectory processing modes such as Gaussian fitting, Fourier transform filtering and Winsorizing method to suppress trajectory distortion caused by different positioning accuracies of a microscopic characterization device in horizontal and axial directions. The error suppression method can make the suppressed trajectory closer to the actual situation, effectively avoid introducing significant differences in horizontal and axial directions in data processing of the suppressed trajectory, and obtain a three-dimensional motion trajectory of a particle target with the same random jittering degree in horizontal and axial directions. The application solves the problem of three-dimensional motion trajectory distortion of particles caused by different axial positioning accuracies and horizontal directions in the process of three-dimensional tracking of particles due to the limitation of characterization methods. The application is particularly suitable for low-exposure-time high-frame-rate and high-signal-to-noise-ratio systems caused by small samples. The application is suitable for three-dimensional particle tracking technologies based on defocusing imaging such as interference, fluorescence, dark field and digital holography.

[0005] The application is implemented by the following technical solutions.

[0006] An axial positioning error suppression method in three-dimensional microscopic trajectory tracking. The method comprises the following steps.

[0007] S1, acquiring a three-dimensional motion trajectory of particles by using a microscopic characterization device, including a three-dimensional peak searching substep and a three-dimensional scatter point connecting substep;

[0008] S2, performing isotropic positioning optimization on peak searching parameters of three orthogonal motion directions of the three-dimensional motion trajectory based on Gaussian fitting to obtain a positioning-optimized three-dimensional motion trajectory;

[0009] S3, performing Fourier transform high-order filtering axial positioning error suppression on abnormal high-frequency one-way repeated jittering in the three-dimensional motion trajectory;

[0010] S4, performing differential on the three-dimensional motion trajectory to obtain axial instantaneous velocity, performing normality test on the distribution of the instantaneous velocity, and performing Winsorizing method-based axial positioning error suppression on the three-dimensional motion trajectory;

[0011] S5, performing Gaussian distribution fitting on instantaneous velocities of three directions of the three-dimensional motion trajectory, correcting abnormal distribution caused by positioning error according to the ratio of standard deviations of each direction, and performing axial positioning error suppression on the axial instantaneous velocity distribution based on Gaussian distribution statistical parameters;

[0012] S6, obtaining a three-dimensional motion trajectory of a particle target with the same random jittering distribution degree in horizontal and axial directions.

[0013] Further, in the step S1, the three-dimensional motion trajectory of the microparticle is acquired by using a microscopic characterization device, and the axial positioning accuracy and the horizontal positioning accuracy of the microscopic characterization device for the microparticle are different.

[0014] Further, in the step S2, the peak-seeking position is determined by using a Gaussian distribution fitting method for the light intensity as the peak-seeking parameter, and the positioning in each direction is optimized, and the fitting calculation formula is as follows:

[0015]

[0016] wherein I is the peak-seeking parameter in a certain range around the original three-dimensional motion trajectory, and here is the light intensity; I0 is the background noise level of the peak-seeking parameter; z0 is the original three-dimensional peak-seeking position; the to-be-fitted parameter A is the peak height parameter; the to-be-fitted parameter σ is the standard deviation of the peak-seeking parameter, reflecting the distribution width of the peak-seeking parameter; and the to-be-fitted parameter z G is the three-dimensional position after the Gaussian distribution fitting.

[0017] Further, in the step S3, the three-dimensional motion trajectory to be suppressed is subjected to high-order filtering processing by Fourier transform, and the calculation formula is as follows:

[0018]

[0019] wherein z[n] is the original time-domain input; N is the length of the input vector; Z[k] is the transformed frequency-domain output; k is the index of the current frequency component, ranging from 1 to N; and the inverse Fourier transform formula after filtering is as follows:

[0020]

[0021] wherein Z[k] is the frequency-domain input; N is the length of the input vector; z[n] is the time-domain output; and n is the index of the current time component, ranging from 1 to N.

[0022] Further, each three-dimensional motion trajectory should contain three-dimensional coordinate information and a defocus distance of a certain microparticle (including a solid particle, a micro-nano bubble, a micro-nano bubble or a microorganism) at a plurality of time nodes within a certain time period.

[0023] Further, the maximum defocus distance of the three-dimensional motion trajectory should be within the depth of field range allowed by the microscopic characterization device.

[0024] Further, the positioning accuracy of the horizontal direction and the axial direction of the microscopic characterization device for the acquired three-dimensional motion trajectory of the microparticle can be considered as not changing with time in a single or single series of three-dimensional motion trajectory characterization experiments.

[0025] Further, in step S5, the axial positioning error suppression method of the Gaussian distribution statistical parameters is as follows: for the three-dimensional motion trajectory processed by the above steps, the instantaneous velocities in the horizontal direction and the axial direction are obtained, and the instantaneous velocities in the three directions are fitted by Gaussian distribution, and the fitting formula is as follows:

[0026]

[0027] Wherein, v and v0 are the instantaneous velocities in one direction before and after fitting respectively, P is the probability value of the distribution, P0 is the probability reference value, w is the overall standard deviation of the Gaussian distribution, and B is the proportional coefficient. v0, P0, w, and B are parameters to be fitted.

[0028] Compared with the prior art, the advantages of the present application are as follows:

[0029] The present application first proposes a method for suppressing three-dimensional motion trajectory distortion caused by system errors of a microscopic characterization device. Compared with the trajectory smoothing method of averaging the three-dimensional motion trajectory in the range, the present method focuses on screening out data greatly affected by system errors and correcting these data, which can better preserve the real speed and acceleration characteristics of the original three-dimensional motion trajectory. It is suitable for systems with low exposure time, high frame rate, and small sample, which are more susceptible to system errors due to high signal-to-noise ratio and measurement results. It is suitable for various particle three-dimensional motion trajectory tracking technologies based on interference, fluorescence, dark field digital holography, etc. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a flow chart of the axial positioning error suppression method in the three-dimensional microscopic trajectory tracking described in the present application;

[0031] Figure 2 is a comparison chart of the three-dimensional motion trajectory of the polystyrene standard microspheres dispersed in water in Example 1 before and after trajectory suppression;

[0032] Figure 3 is a comparison chart of the MSD results of the polystyrene standard microspheres dispersed in water in Example 1 before and after trajectory suppression.

[0033] Figure 4 is a comparison chart of the three-dimensional motion trajectory of the polystyrene standard microspheres dispersed in liquid crystal in Example 2 before and after trajectory suppression. DETAILED DESCRIPTION

[0034] The following is an embodiment of the method for suppressing three-dimensional motion trajectory distortion caused by characterization device system errors proposed in the present application with reference to the accompanying drawings. However, the embodiments of the present application are not limited thereto.

[0035] Example 1

[0036] A method for optimizing the axial positioning of microparticles based on error suppression, as shown in Figure 1 comprises the following steps.

[0037] S1, obtaining the three-dimensional motion trajectory of the sample. Prepare a microparticle, microbubble or microorganism sample and observe it under a microscopic characterization device that can characterize its three-dimensional motion trajectory, record a series of images of the microparticle in real time containing three-dimensional motion trajectory information (here, the information refers to kinematic information such as velocity, acceleration, mean square end displacement, etc.) using an optical sensor. The sample in this embodiment uses polystyrene standard microspheres with an average particle size of 0.96 μm dispersed in ultrapure water, and the microsphere concentration is 10 7 / mL. The three-dimensional microscopic characterization device uses a digital holographic microscope; the light source selects a LED light source with a center wavelength of 365 nm, a 100x objective lens, and the camera parameters are set as follows: the frame rate is set to 40 fps, the exposure time is 0.025 s, and the image resolution is 1024x1024; 2400 optical interference gray-scale original images with a bit depth of 16 are continuously taken, and the square field of view range of each optical interference original image is 66.56 μm long, and the length of a single pixel after magnification is 65 nm. The three-dimensional peak finding sub-step and the three-dimensional scatter point connecting sub-step are as follows: calculate and restore the three-dimensional light field of the polystyrene standard microspheres with an average particle size of 0.96 μm in each frame based on the light propagation principle, find the peak in the three-dimensional light field by the maximum light intensity criterion, and obtain the preliminary three-dimensional position information of the polystyrene standard microspheres; according to the space-time consistency principle, the coordinate position information of the microspheres obtained in each frame, which is in the form of three-dimensional scatter points, is connected into a three-dimensional motion trajectory; the following axial positioning error suppression in this embodiment will be carried out around these trajectories.

[0038] S2, respectively optimizing the positioning in each direction based on Gaussian fitting of the peak finding parameter distribution of the three orthogonal motion directions of the three-dimensional motion trajectory. According to the guidance of the three-dimensional motion trajectory, the light intensity information of the three-dimensional light field within a radius of 32 pixels around the three-dimensional motion trajectory itself is obtained by the camera original image and the three-dimensional light field reconstruction program based on the light propagation principle, and the light intensity information is the peak finding parameter; the distribution curve of the light intensity is obtained in the X, Y horizontal directions and the axial direction with the three-dimensional coordinates given by the trajectory as the center; the peak finding positioning position of the light intensity as the peak finding parameter is confirmed by the Gaussian distribution fitting method, the positioning in each direction is optimized, and the light intensity distribution curve is fitted based on the least squares method using the following Gaussian distribution formula:

[0039]

[0040] Wherein, I is the peak-seeking parameter within a certain range around the original track, here is the light intensity of the three-dimensional light field; I0 is the background noise level of the three-dimensional light intensity, which is obtained by averaging the light intensity values of 80% of the darker part of the entire three-dimensional light field; z0 is the three-dimensional coordinate position given by the track, i.e. the original three-dimensional peak-seeking position, here the axial position is taken as an example; the to-be-fitted parameter A is the peak height parameter; the to-be-fitted parameter σ is the standard deviation of the peak-seeking parameter, reflecting the distribution width of the peak-seeking parameter; the to-be-fitted parameter z G is the axial position of the microsphere in this frame after Gaussian distribution fitting. The positioning optimization steps of Gaussian fitting in the X and Y horizontal directions are the same as above. After fitting the distribution curves of light intensity in the horizontal direction and the axial direction as described above, the central peak coordinates are obtained, i.e. the three-dimensional coordinates of the positioned and optimized micro-particles. The above operations are repeated for each frame of the three-dimensional motion track to obtain the three-dimensional motion track of the positioned and optimized micro-particles.

[0041] S3, axial positioning error suppression by Fourier transform high-order filtering of abnormal high-frequency one-way repetitive jitter in the three-dimensional motion track. Since most micro-particles, micro-bubbles or microorganisms will not perform long-time high-frequency jitter motion in a certain direction without external conditions, the same applies to polystyrene standard microspheres without external conditions. The occurrence of such high-frequency jitter can determine the occurrence of regular abnormal axial positioning. Therefore, for the axial positioning result with the largest jitter degree in the three-dimensional motion track, the axial instantaneous velocity information is obtained by differentiating the axial position, and one-dimensional Fourier transform is performed. The formula used for Fourier transform high-order filtering processing of the three-dimensional motion track is as follows:

[0042]

[0043] Wherein, z[n] is the original time-domain input, here is the axial position at time n after Gaussian fitting and positioning optimization; N is the length of the input vector, since the difference method is used for calculation speed, the vector length is 2399 here; Z[k] is the frequency domain output after Fourier transform; k is the index of the current frequency component, ranging from 1 to 2399, i is the imaginary unit;

[0044] For the high-frequency data reaching the highest frequency of 50%, the abnormal high-frequency peak is removed. For most particles, regular high-frequency jitter is abnormal, and high-frequency data is generally close to 0. Here, the high-frequency data greater than twice the average of all high-frequency data is removed; then one-dimensional inverse Fourier transform is performed to obtain the Fourier transform high-order filtered axial instantaneous velocity. The formula for filtered inverse Fourier transform is as follows:

[0045]

[0046] Where, Z[k] is the frequency domain input, k is the frequency domain value; N is the length of the input vector, here the vector length is 2399; z'[n] is the time domain output; n is the index of the current time component, ranging from 1 to 2399, i is the imaginary unit. After transformation, the axial motion trajectory and the three-dimensional motion trajectory can be further obtained according to the following steps.

[0047] S4, axial positioning error suppression based on Winsorizing method. Winsorizing method is a method for making a group of data not following Gaussian distribution more consistent with Gaussian distribution by modifying extreme values. The three-dimensional motion trajectory is differentiated to obtain the axial instantaneous velocity, and the axial instantaneous velocity information of each frame of the axial data of the three-dimensional motion trajectory processed in the previous step is extracted. The normality test is performed on the distribution of the instantaneous velocity. If the result of the normality test is less than 0.05 (indicating that the current data is not significantly from a normal distribution population), the 5% and 95% quantiles of the current instantaneous velocity distribution are further determined, and Winsorizing data processing is performed. Winsorizing data processing is a signal processing method for clipping abnormal values, which limits the extreme value in the statistical data to reduce the influence of possible false abnormal values, thereby converting the statistical data. The instantaneous velocity after axial positioning error suppression based on Winsorizing method is obtained, the axial motion trajectory is obtained by integrating the velocity, and the three-dimensional motion trajectory is obtained by combining the horizontal direction motion trajectory.

[0048] S5, axial positioning error suppression of Gaussian distribution statistical parameters for the distribution of the instantaneous velocity in the two horizontal directions and the axial direction. For the three-dimensional motion trajectory processed in the previous steps, the instantaneous velocity in the horizontal direction and the axial direction is obtained, and the instantaneous velocity in the three directions is fitted according to the Gaussian distribution. The fitting formula is as follows:

[0049]

[0050] Where, v and v0 are the instantaneous velocity in one direction before and after fitting respectively, P is the probability value of the distribution, P0 is the probability reference value, w is the standard deviation of the Gaussian distribution population, and B is the proportional coefficient. v0, P0, w, and B are parameters to be fitted. Here we mainly focus on the fitting parameter w.

[0051] The fitting is performed to obtain three groups of Gaussian distribution parameters in three directions, each group of parameters including the mean and standard deviation of the instantaneous velocity distribution in the direction; if the standard deviation of the axial direction and the two standard deviations of the horizontal direction still have significant differences, that is, the means are significantly different at the 0.05 level in the analysis of variance, the standard deviation of the axial velocity is equal to the average of the two standard deviations of the horizontal direction; in this way, each axial instantaneous velocity is changed, and the axial trajectory after the axial positioning error of the Gaussian distribution statistical parameters is suppressed is obtained by the definite integral, combined with the horizontal trajectory as the reference for positioning error suppression, to obtain the three-dimensional motion trajectory.

[0052] S6, obtaining the three-dimensional motion trajectory of the microparticle target with the same random jitter degree in the horizontal direction and the axial direction after completing the positioning error suppression corresponding to the original trajectory. Select a typical trajectory, and the comparison diagram of the trajectory and the original trajectory is as follows Figure 2 It can be seen from the comparison that the abnormal positioning jitter in the axial direction of the original trajectory is effectively suppressed, and the processed trajectory is more consistent with the classical Brownian motion trajectory. Figure 3 According to

[0053] Example 2

[0054] The sample in Example 1 is changed to a liquid crystal with a viscosity of 40 mPa·s and containing 0.2 μm polystyrene standard microspheres with an average particle size of 0.2 μm, and the concentration of the microspheres is 10 8 / mL.

[0055] The light source is an LED light source with a center wavelength of 505 nm, a 100 times objective lens, and the camera parameters are set as follows: the frame rate is set to 40 fps, the exposure time is 0.025 s, the image resolution is 1024×1024, 12000 gray-scale optical interference figure original images with a bit depth of 16 are continuously shot, the square field of view range of each optical interference original image has a side length of 66.56 μm, and the unit pixel length after magnification is 65 nm. The position information of the polystyrene standard microspheres in space is calculated and restored based on the propagation principle of light, and the three-dimensional motion trajectory of the Brownian motion of the microspheres in the liquid crystal is obtained.

[0056] In the axial positioning error suppression of the three-dimensional motion trajectory, compared with Example 1, in step S5, the standard deviation of the axial velocity is not directly equal to the average of the two standard deviations of the horizontal direction, but the axial velocity is multiplied by a parameter, which is from the ratio of the axial velocity standard deviation of the polystyrene standard microspheres to the two standard deviations of the horizontal direction under the same experimental conditions and defocusing distance. The rest of the experimental and data processing steps and the used formulas and parameters are unchanged.

[0057] After the above image capturing and data processing process, the three-dimensional motion trajectory of the particle with the same degree of horizontal and axial random jitter corresponding to the original trajectory and completing the positioning error suppression is obtained. A typical trajectory is selected, and a comparison diagram of the trajectory and the original trajectory is as follows Figure 4 It can be seen from the comparison that the axial abnormal positioning jitter in the original trajectory is effectively suppressed, and the processed trajectory can still reflect the anisotropic properties of the liquid crystal medium.

[0058] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present application should be equivalent replacement methods, and are all included in the protection scope of the present application.

Claims

1. A method for suppressing axial positioning errors in three-dimensional microscopic trajectory tracking, characterized in that: The following steps are involved: S1, obtaining the three-dimensional motion trajectory of the particle; S2, perform Gaussian fitting in three orthogonal motion directions; S3, performing Fourier transform high-order filtering to suppress axial positioning errors; S4, perform normality test and axial positioning error suppression based on Winsorizing method; S5. Suppressing the axial positioning error using Gaussian distribution statistical parameters; In step S5, the distribution of the instantaneous velocities in the two horizontal directions and the axial direction is subjected to axial positioning error suppression using the statistical parameters of the Gaussian distribution. For the three-dimensional motion trajectory processed by the above steps, the instantaneous velocities in the horizontal direction and the axial direction are obtained, and Gaussian distribution fitting is performed on the instantaneous velocities in the three directions. The fitting formula is as follows: ； Where v and v0 are the instantaneous velocities in one direction before and after fitting, respectively; P is the probability value of the distribution; P0 is the probability reference value; w is the overall standard deviation of the Gaussian distribution; B is the proportional coefficient; v0, P0, w, and B are all parameters to be fitted; S6. Obtain a three-dimensional motion trajectory of the particle target with the same degree of random jitter in the horizontal direction and the axial direction.

2. The method for suppressing axial positioning errors in three-dimensional microscopic trajectory tracking according to claim 1, characterized in that: The microparticles include solid particles, micro-nano bubbles, micro-nano vacuoles and microorganisms.

3. The method for suppressing axial positioning errors in three-dimensional microscopic trajectory tracking according to claim 1, characterized in that: In step S1 , obtaining the three-dimensional motion trajectory of the particle consists of a three-dimensional peak search sub-step and a three-dimensional scattered point connection sub-step.

4. The method for suppressing axial positioning errors in three-dimensional microscopic trajectory tracking according to claim 1, characterized in that: In step S2, the peak search parameters are fitted based on Gaussian distribution to confirm the peak search location and optimize the positioning in all directions. The fitting calculation formula is as follows: ； Where I is the peak-finding parameter within a certain range around the original trajectory; I0 is the background noise level of the peak-finding parameter; z0 is the original three-dimensional peak-finding position; the parameter to be fitted A is the peak height parameter; the parameter to be fitted σ is the standard deviation of the peak-finding parameter, which reflects the distribution width of the peak-finding parameter; the parameter to be fitted z G is the three-dimensional position after Gaussian distribution fitting.

5. The method for suppressing axial positioning errors in three-dimensional microscopic trajectory tracking according to claim 1, characterized in that: In step S3, the three-dimensional motion trajectory to be suppressed is subjected to Fourier transform high-order filtering, and the calculation formula is as follows: ； Where z[n] is the original time domain input; N is the length of the input vector; Z[k] is the transformed frequency domain output; k is the index of the current frequency component, ranging from 1 to N; the inverse Fourier transform formula after filtering is as follows: ； Where Z[k] is the frequency domain input; N is the length of the input vector; z[n] is the time domain output; and n is the index of the current time component, ranging from 1 to N.

6. The method for suppressing axial positioning errors in three-dimensional microscopic trajectory tracking according to claim 1, characterized in that: The Winsorizing method described in step S4 is a signal processing method for clipping outliers, which reduces the influence of possible false outliers by limiting the extreme values ​​in the statistical data, thereby transforming the statistical data.

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