CN119359819A - Projection parameter calibration method for fiducial marker alignment in cryo-electron microscopy images - Google Patents
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Abstract
The invention provides a projection parameter calibration method in the alignment of a frozen electron microscope image reference mark, and belongs to the technical field of electron microscope image processing. The invention provides a new robust projection parameter calibration model based on the property of L 1 norm and Laplace noise assumption to break through the defects of the traditional robust method, thereby being capable of better reducing the influence of noise and outlier pollution in calibration point data. The method and the device are based on the Laplace noise assumption, more in line with noise and outlier distribution in the calibration point data, the numerical scheme based on the smoothing strategy can iteratively approach the original problem, can solve the problem more quickly and stably, and accordingly can carry out robust calibration of projection parameters quickly and stably, and the problem of poor calibration effect caused by incomplete calibration point data optimization or unreasonable weight distribution in the traditional robust scheme is avoided.
Description
Technical Field
The invention relates to the technical field of electron microscope image processing, in particular to a projection parameter calibration method in frozen electron microscope image reference mark alignment.
Background
In the three-dimensional reconstruction of the frozen electron microscope image, a reference point alignment technology automatically aligns image sequences of different angles by using colloidal gold particles in a sample as calibration points, so that the method has wide research and application.
The projection parameter calibration is used as the final step of the reference point alignment technology, and the projection parameters of each picture and the space point coordinates of each colloidal gold particle are optimized by using the calibration point position data measured by the pre-step. However, due to inaccurate positioning or incorrect matching of the calibration points, the measured calibration point data usually contains noise and outlier pollution, which affects the effect of parameter calibration to a certain extent. Therefore, how to perform robust parameter calibration so as to reduce the influence of noise and outliers in calibration point data is an important research problem for improving the alignment accuracy of the frozen electron microscope image.
For the above problems, there are two common robust parameter calibration schemes. One approach is to iteratively optimize the calibration point data using probabilistic statistical analysis or spatial geometry analysis techniques to remove noise and outliers from the data, but such methods are generally not perfect for removing contamination from the data. Another approach is to introduce an iterative least squares technique with weights, assign weights of 0 to 1 to each calibration point based on statistical analysis of the residual distribution of the calibration points and iterate the calibration multiple times, but such methods may affect the final effect due to unreasonable weight assignment. In addition, the mathematical models of the two conventional robust calibration techniques are established based on the assumption that noise in the calibration point data is gaussian. However, in practical application, since the accuracy of locating the calibration point is mainly affected by the imaging quality of the point, the noise distribution in the calibration point data should be more prone to a part of points being more noisy and the rest of points being less noisy, and the outlier caused by incorrect matching will increase the tendency of the "two-head distribution", so the laplace distribution that is more "extreme" should be closer to the noise distribution in the calibration point data. Based on Laplacian assumption of calibration point data noise, a binding adjustment model based on L 1 norm can be established to perform robust parameter calibration, but the existing model numerical solving method has higher running loss and instability, and cannot meet the application of the field of frozen electron microscope microscopic image alignment.
Disclosure of Invention
The invention aims to provide a projection parameter calibration method in the alignment of a frozen electron microscope image reference mark, which utilizes a robust projection parameter calibration model to reduce the influence of noise and outliers in calibration point data on the image alignment effect so as to overcome the limitation of a traditional robust model and solve the problems of low efficiency and instability of the existing solving scheme.
In order to achieve the purpose, the invention adopts the following specific technical scheme:
A projection parameter calibration method in frozen electron microscope image reference mark alignment comprises the following steps:
s1, taking measured calibration point data and initial estimation of projection parameters as inputs;
S2, establishing a binding adjustment model of L 1 norms based on the minimized re-projection residual error to obtain a non-convex non-smooth optimization problem;
s3, obtaining a smooth approximation problem based on a smoothing strategy;
And S4, carrying out iterative numerical solution on the smooth approximation problem to obtain a final reconstruction result.
Further, in the step S1, a microscope shoots a biological sample containing m colloidal gold particles from n different angles to obtain an image sequence, q ij＝(uij,vij)T is defined as a standard point obtained by imaging the jth colloidal gold particle in the ith image, C i is a projection parameter of the ith image, X j＝(xj,yj,zj)T is a space point coordinate ,C＝(C1,C2…Cn)T,X＝(X1,X2…Xm)T,E＝(C,X)T,pij＝(ui′j,vi′j)T＝Proj(Ci,Xj) of the jth colloidal gold particle and is a re-projection of the jth colloidal gold particle in the ith image.
Further, in S2, the following bundled tuning model of the L 1 norm is constructed by using the laplace noise hypothesis and the properties of the L 1 norm:
Wherein ii 1 is the L 1 norm.
Further, in the step S3, the smoothing approximation problem is derived:
Smoothing approximation, namely, the non-smoothness in the L 1 norm binding model comes from an absolute value function f (x) = |x| and a smoothing function is selected Approximating it, where τ is called the smoothing parameter, thus yielding an approximate optimization problem for the bundled-tuning model of the L 1 norm:
And (3) a smoothing parameter updating strategy, namely, for a smoothing parameter tau in the approximation problem, giving an initial value tau 0 (a default value is 1), iteratively reducing the value of the smoothing parameter tau so as to gradually approach the approximation problem to the original problem, wherein the following updating strategy is adopted, and the updating time of the smoothing parameter is that the following inequality is established:
Wherein the method comprises the steps of Representation ofGradient at point E, omega value defaults to 1000, smoothing parameters are updated in the following way:
τk+1＝δτk
where δ defaults to 0.05.
Further, in the step S4, the numerical solution method includes:
S4-1 smooth gradient method
For approximation, iterative numerical solution using gradient method with Armijo line search is described as follows, for the kth iteration, the forward direction g k is the negative gradient direction of the current position E k Step α k is the maximum value in the set { ρ 0,ρ1,ρ2..} (ρdefault to 0.5) that satisfies the following inequality:
The updating of each step of iteration parameters is as follows:
Ek+1＝Ek+αkgk
S4-2:Z-score normalization
In order to improve the stability of the algorithm, preprocessing data by adopting Z-score normalization, carrying out data recovery by adopting inverse normalization after iteration solution is finished, recording the mean value of the coordinate data of the standard point obtained by measurement as mu, the standard deviation as sigma, and describing the normalization process as follows:
the inverse normalization process is the inverse of the above process.
Compared with the prior art, the invention has the beneficial effects that:
The invention provides a new robust projection parameter calibration model based on the property of L 1 norm and Laplace noise assumption to break through the defects of the traditional robust method, thereby being capable of better reducing the influence of noise and outlier pollution in calibration point data. The method and the device are based on the Laplace noise assumption, more in line with noise and outlier distribution in the calibration point data, the numerical scheme based on the smoothing strategy can iteratively approach the original problem, can solve the problem more quickly and stably, and accordingly can carry out robust calibration of projection parameters quickly and stably, and the problem of poor calibration effect caused by incomplete calibration point data optimization or unreasonable weight distribution in the traditional robust scheme is avoided.
Drawings
Fig. 1 is a schematic view of projection parameter calibration based on minimizing the re-projection residual.
Fig. 2 is a basic flow chart of the method of the present invention.
Fig. 3 is a schematic diagram of the published data set employed in example 2.
Detailed Description
The technical scheme of the invention is further described and illustrated below by combining with the embodiment.
Example 1
Projection parameter calibration is typically achieved by minimizing the residual between the measured coordinates of the calibration point and the estimated re-projection coordinates of the spatial point, as shown in fig. 1. When the measurement of the calibration point data is performed, noise is generated due to inaccurate positioning in the positioning stage, outliers are generated due to incorrect matching in the matching stage, and the final alignment effect is affected by the noise and the outliers. Both existing robust solutions have their own limitations and are based on gaussian noise assumptions that may not be appropriate.
The invention obtains a new robust calibration model by utilizing the property of L 1 norm and Laplace noise assumption, and designs a new numerical solution scheme based on a smoothing strategy, as shown in figure 2, the specific model construction, smoothing approximation strategy and the numerical solution method are as follows:
1L 1 norm binding and adjusting model construction:
1.1 basic concept assuming that a microscope shoots a biological sample containing m colloidal gold particles from n different angles to obtain an image sequence, q ij＝(uij,vij)T is defined as a standard point obtained by imaging the jth colloidal gold particle in the ith image, C i is a projection parameter of the ith image, X j＝(xj,yj,zj)T is a space point coordinate ,C＝(C1,C2…Cn)T,X＝(X1,X2…Xm)T,E＝(C,X)T,pij＝(u′ij,v′ij)T＝Proj(Ci,Xj) of the jth colloidal gold particle and is a re-projection of the jth colloidal gold particle in the ith image.
1.2 Projection model construction the invention is applicable to all projection models, an example being given here to illustrate the details of the calculation of p ij. Assuming that C i＝(si,αi,βi,γi,t1i,t0i)T is a projection parameter of the i-th image, where s represents a change in a dimension of the projection image, γ represents an in-slice rotation of the projection image, α represents a tilting angle of the projection image around a rotation axis during imaging, β represents a tilting angle of the projection image around the rotation axis during imaging, and t 0 and t 1 represent translational variables in x-direction and y-direction of the projection image, the orthographic projection model may be expressed as:
Wherein:
1.3 re-projection residual construction in general, projection parameter calibration is converted into a bundled tuning model, described as the following least squares problem that minimizes the re-projection residual:
Where ψ (.) is the residual function, d (.) is the distance function, Φ ij is the mask indicating whether the calibration point is visible, and the value is 0 or 1. Using the Laplace noise hypothesis and the properties of the L 1 norm, a bundled tuning model of the L 1 norm is constructed as follows:
Wherein ii 1 is the L 1 norm.
2 Smoothing approximation problem derivation:
2.1 smoothing approximation-non-smoothness in the L 1 -norm bundled model comes from the absolute value function f (x) = |x| and we choose the smoothing function Approximation is made of this, where τ is referred to as the smoothing parameter. Thus, an approximate optimization problem of the bundled shape model of L 1 norms is obtained:
2.2 smoothing parameter update strategy for smoothing parameter τ in the approximation problem, given an initial value τ 0 (default value 1), its value is iteratively scaled down so that the approximation problem gradually approaches the original one, here the following update strategy is employed. The update timing of the smoothing parameter is that the following inequality holds:
Wherein the method comprises the steps of Representation ofGradient at point E, ω defaults to 1000. Update of smoothing parameters:
τk+1＝δτk
where δ defaults to 0.05.
3, A numerical solution method:
3.1 smooth gradient method
For approximation, iterative numerical solution using gradient method with Armijo line search is described as follows, for the kth iteration, the forward direction g k is the negative gradient direction of the current position E k Step α k is the maximum value in the set { ρ 0,ρ1,ρ2..} (ρdefault to 0.5) that satisfies the following inequality:
The updating of each step of iteration parameters is as follows:
Ek+1＝Ek+αkgk.
3.2Z-score normalization
In order to improve the stability of the algorithm, preprocessing data by adopting Z-score normalization, carrying out data recovery by adopting inverse normalization after iteration solution is finished, recording the mean value of the coordinate data of the standard point obtained by measurement as mu, the standard deviation as sigma, and describing the normalization process as follows:
the inverse normalization process is the inverse of the above process.
Example 2:
In the embodiment, four sets of public data sets with different characteristics and different scales are selected, and a V-1Gag data set, a VEEV data set, a Centriole data set and an SNX3 data set are compared with a common LM method and an existing L 1 interior point method for experiments, wherein images of the four sets of public data sets at 0 degrees are shown in figure 3.
Table 1 method comparison results on different data sets
For each set of data set, software Markerauto is adopted to perform the processing before calibration, including calibration point detection, matching, initial estimation of projection parameters and the like, and initial estimation of the coordinates of the space points of the colloidal gold particles is obtained through triangulation. The experimental results are shown in table 1. In the method efficiency, the time consumption of the smoothing method is far lower than that of the interior point method, and the memory consumption is the lowest, so that the method has high efficiency and low loss, and has practical application prospect. The above results all demonstrate the high robustness and high efficiency of the L 1 smoothing process of the present invention.
Finally, although the description has been described in terms of embodiments, not every embodiment is intended to include only a single embodiment, and such description is for clarity only, as one skilled in the art will recognize that the embodiments of the disclosure may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (5)
1. A method for calibrating projection parameters in alignment of reference marks of images of a frozen electron microscope, comprising the following steps:
s1, taking measured calibration point data and initial estimation of projection parameters as inputs;
S2, establishing a binding adjustment model of L 1 norms based on the minimized re-projection residual error to obtain a non-convex non-smooth optimization problem;
s3, obtaining a smooth approximation problem based on a smoothing strategy;
And S4, carrying out iterative numerical solution on the smooth approximation problem to obtain a final reconstruction result.
2. The projection parameter calibration method according to claim 1, wherein in S1, an image sequence is obtained by shooting a biological sample containing m colloidal gold particles from n different angles, q ij＝(uij,vij)T is defined as a calibration point obtained by imaging the jth colloidal gold particle in the ith image, C i is a projection parameter of the ith image, X j＝(xj,yj,zj)T is a space point coordinate ,C＝(C1,C2…Cn)T,X＝(X1,X2…Xm)T,E＝(C,X)T,pij＝(ui′j,vi′j)T＝Proj(Ci,Xj) of the jth colloidal gold particle and is a re-projection of the jth colloidal gold particle in the ith image.
3. The projection parameter calibration method according to claim 1, wherein in S2, using the laplace noise hypothesis and the properties of the L 1 norm, a bundled tuning model of the L 1 norm is constructed as follows:
Wherein ii 1 is the L 1 norm.
4. The projection parameter calibration method according to claim 1, wherein in the step S3, the smoothing approximation problem is deduced that the non-smoothness in the smoothing approximation L 1 norm bundled model is derived from an absolute value function f (x) = |x| and a smoothing function is selectedApproximating it, where τ is called the smoothing parameter, thus yielding an approximate optimization problem for the bundled-tuning model of the L 1 norm:
the following update strategy is adopted, and the update time of the smoothing parameters is established as follows:
Wherein the method comprises the steps of Representation ofGradient at point E, omega value defaults to 1000, smoothing parameters are updated in the following way:
τk+1＝δτk
where δ defaults to 0.05.
5. The projection parameter calibration method according to claim 1, wherein in S4, the numerical solution method is as follows:
S4-1 smooth gradient method
For approximation, iterative numerical solution is performed using a gradient method with Armijo line search, in which for the kth iteration, the heading g k is the negative gradient direction of the current position E k Step α k is the maximum value in the set { ρ 0,ρ1,ρ2..} (ρdefault to 0.5) that satisfies the following inequality:
The updating of each step of iteration parameters is as follows:
Ek+1＝Ek+αkgk
S4-2:Z-score normalization, preprocessing data by adopting Z-score normalization, carrying out data recovery by adopting inverse normalization after iteration solution is finished, recording the mean value of coordinate data of a standard point obtained by measurement as mu, the standard deviation as sigma, and describing the normalization process as follows:
the inverse normalization process is the inverse of the above process.
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