Adaptive filtering weighted sub-tomogram iteration alignment method
By using an adaptive filtering-weighted sub-tomogram iterative alignment method, the problem of insufficient alignment accuracy caused by low signal-to-noise ratio and missing wedge effect in cryo-electron computed tomography is solved, and efficient and accurate three-dimensional structure reconstruction is achieved.
Patent Information
- Application Number
- CN202610064180.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-19
- Publication Date
- 2026-05-01
Smart Images
Figure CN121962359A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of cryo-electron microscopy image processing, and in particular to an adaptive filtering weighted sub-tomogram iterative alignment method. Background Technology
[0002] Cryo-electron tomography (Cryo-ET) is widely used in structural biology to resolve the three-dimensional structures of macromolecular complexes in situ within cells. However, because tomographic images typically have low resolution, sub-tomographic averaging (STA) is necessary to improve image quality. Sub-tomographic alignment is a crucial step, aiming to accurately calculate the translation and rotation parameters of sub-volumes within a series of tomographic images, thereby improving the final reconstruction accuracy. The accuracy of sub-tomographic alignment directly determines the quality of the final 3D structure, especially when processing cryo-electron microscopy tomographic data with low signal-to-noise ratios and significant wedge-shaped defects. This process typically relies on initial projection parameter estimation and iterative optimization algorithms to progressively correct the pose parameters of each sub-image.
[0003] The challenges in aligning sub-tomograms stem from two inherent defects in Cryo-ET data: low signal-to-noise ratio (SNR) and missing wedge effect. Low SNR obscures the feature correspondences between sub-tomograms, significantly increasing the difficulty of accurately calculating their relative orientations and positions. The missing wedge effect, on the other hand, results in sub-tomograms with different orientations containing incomplete or inconsistent structural information, causing severe distortion when using traditional cross-correlation functions as alignment criteria. Under these conditions of incomplete information and heavy noise contamination, standard alignment algorithms are prone to getting trapped in erroneous local extrema, leading to incorrect estimations of the sub-tomogram projection parameters and ultimately resulting in low 3D reconstruction resolution or even misleading structural features.
[0004] To address the low signal-to-noise ratio (SNR) problem, existing technologies generally employ frequency-domain low-pass filtering to suppress high-frequency noise and rely on iterative refinement and 3D classification to gradually improve the quality of the reference model. However, while filtering reduces noise, it inevitably loses crucial high-resolution structural information, and the iterative process is extremely sensitive to initial alignment errors, easily amplifying deviations at very low SNRs, causing the algorithm to get trapped in local optima.
[0005] To address the missing wedge effect, common methods include introducing a corresponding wedge mask into the reference model during cross-correlation calculations or generating a simulated template containing the same missing wedge effect for matching. However, this compensation mechanism is too coarse. Its binary "either / or" approach simply discards any information possibility within the missing wedge region, ignoring the reliability differences in actual retained frequency information due to noise and CTF attenuation. This method fails to achieve refined weighting of available information. When the sub-tomogram severely overlaps with the missing region of the reference model, the effective signal bandwidth becomes too narrow, and the matching capability of traditional cross-correlation algorithms deteriorates sharply, leading to a decrease in alignment accuracy. Summary of the Invention
[0006] The purpose of this invention is to provide an adaptive filtering weighted sub-tomogram iterative alignment method to overcome the shortcomings of the prior art.
[0007] In traditional cryo-electron microscopy tomography alignment, errors in the calculation of rotation and translation parameters may occur due to the low signal-to-noise ratio of the original data and the missing wedge effect, resulting in poor accuracy of the average results of subsequent sub-tomograms. This invention provides an iterative alignment method that proactively improves signal quality and adaptively weights frequency information based on confidence. It quantifies the similarity between sub-tomograms and the reference model using cross-correlation calculations based on Fast Fourier Transform, employs a coarse-to-fine multi-stage search strategy to efficiently determine global and local optimal solutions, and specifically designs a missing wedge compensation mechanism to overcome the impact of resolution anisotropy caused by the missing wedge effect on alignment accuracy.
[0008] To achieve the above objectives, the present invention adopts the following technical solution:
[0009] An adaptive filtering-weighted sub-tomogram iterative alignment method includes the following steps: S1: Acquire cryo-electron microscopy tomographic image data and initial pose parameters, and perform data preprocessing; S2: Generate a list of Euler rotation angles within a given angle range and step size; S3: Adaptive filtering and weighting are applied to the preprocessed sub-tomographic images and the reference model, and coarse alignment is performed: the cross-correlation matrix and translation parameters are calculated in the frequency domain space based on Fourier transform, and the Euler angle corresponding to the maximum cross-correlation value is selected as the optimal rotation angle. S4: Based on the coarsely aligned Euler angles, reduce the step size to generate a new Euler list; S5: Perform fine alignment under the new Euler list to obtain the optimal rotation and translation parameters, and complete the alignment.
[0010] Furthermore, S1 includes: S1-1: First, perform dimensionality checks on the input sub-tomographic images, reference models, various masks, and other data, and fill the smaller-dimensional 3D volumes into larger dimensions to ensure consistent dimensionality. S1-2: Centroid correction process based on high signal-to-noise ratio density region for the reference model; First, low-pass filtering and median filtering are applied to the reference model to suppress noise and preserve the true structural signal; Then, a dynamic thresholding method is used to generate a binary mask by iterative expansion starting from the core density region with the highest signal-to-noise ratio, ensuring that the centroid calculation is based only on the strong signal region and avoiding solvent noise interference; Finally, the weighted average spatial position of the density values within the high-confidence mask is calculated as the corrected centroid; Before comparison, the centroid is aligned with the geometric center of the sub-tomogram to eliminate initial deviations.
[0011] Furthermore, in step S2, the generation of the Euler rotation angle list depends on four parameters. ,in Indicates the range of rotation outside the plane. For the corresponding step size, Indicates the range of rotation within the plane. For the corresponding step size; For each : ; For each ,generate :
[0012] in: ; For each pair ,generate :
[0013] The final list of Euler angles is as follows: .
[0014] Furthermore, in S3, the coarse alignment calculation process involves rotation and translation of the three-dimensional volume. Here, ZXZ order is used to rotate the sub-particles, and trilinear interpolation is used to calculate the three-dimensional volume after rotation and translation. The rotation matrix R is calculated as follows: ; ; in Represents a three-dimensional volume around The angle of rotation of the axis.
[0015] Furthermore, the rotation and translation calculation includes: (1) Pure translation transformation: ; in:
[0016] (2) Pure rotational transformation: ; in It's a data center offset. It is an inverse rotation matrix.
[0017] (3) First translate, then rotate: ; (4) Rotate first, then translate: .
[0018] Furthermore, in S3, an adaptive bandpass filter is applied to the sub-tomographic image. The generation of this filter is a systematic process combining raw data, mathematical models, and prior knowledge. The input data for the entire process includes the raw frequency coordinates, raw FSC values, target frequency coordinates, and a forced mask vector as an artificial constraint. First, the raw FSC values are non-negatively processed. Then, the processed FSC curve is mapped to the target frequency coordinates using cubic spline interpolation. This process employs a clamping function to ensure the interpolation operation is performed safely within the original data frequency range, thereby generating a smooth fitted FSC curve. Subsequently, an MTF correction model is introduced. This model describes the detector's modulation transfer function in exponential form to compensate for the frequency response attenuation of the imaging system. Finally, the results of the preceding steps are integrated: the fitted FSC values are mathematically transformed into FSC weight terms, which are then multiplied by the MTF correction factor and the artificial constraint represented by the forced mask to obtain the final filter cRef(f); that is: .
[0019] Furthermore, in S3, the specific formula for calculating the cross-correlation matrix in the frequency domain is as follows: ; in, Represents a three-dimensional sub-tomogram. Represents the reference model. The wedge mask representing the sub-tomogram. The wedge mask representing the reference model. This represents the inverse Fourier transform. This indicates taking the real part of a complex number.
[0020] Furthermore, the translation parameters are calculated as follows: first, the cross-correlation matrix is masked and filtered: ; Detect the initial peak position: ; The centroid is corrected, and a local window is defined with (maxX, maxY, maxZ) as the center and a radius peakCOM = 3. ; Calculate the centroid offset: ; ; Update peak coordinates: ; The centroid is corrected twice: first using the original coordinates, and then using rounded integer coordinates to improve stability; the final translation parameters are: .
[0021] Furthermore, the calculation of the global cross-correlation value is as follows: ; in, Represents a three-dimensional sub-tomogram. Represents the reference model. The wedge mask representing the sub-tomogram. The wedge mask representing the reference model. Indicates Fourier transform, This indicates taking the real part of a complex number.
[0022] Furthermore, the calculation process for fine alignment in S5 is the same as that for coarse alignment.
[0023] Compared with the prior art, the advantages and beneficial effects of the present invention are:
[0024] (1) The “coarse-to-fine” multi-stage search strategy of the present invention effectively balances computational efficiency and alignment accuracy, and avoids the huge computational overhead caused by global fine search in traditional methods.
[0025] (2) The present invention introduces wedge masks for the sub-tomogram and the reference model respectively, and designs an adaptive bandpass filter to integrate the FSC curve and MTF correction, which effectively compensates for the resolution anisotropy caused by the missing wedge effect and detector attenuation, and significantly improves the alignment accuracy under low signal-to-noise ratio conditions.
[0026] (3) The present invention is based on intelligent centroid correction in high signal-to-noise ratio regions, which can effectively eliminate solvent noise interference and ensure that the initial reference for subsequent rotation and translation calculations is more accurate and reliable.
[0027] (4) The present invention performs two iterations of correction using the weighted centroid method to obtain accurate translation at the sub-pixel level, thereby improving the stability of parameter estimation and the resolution of the final 3D reconstruction. Attached Figure Description
[0028] Figure 1 This is the alignment flowchart of the present invention.
[0029] Figure 2 This is a flowchart of the reference model centroid correction process.
[0030] Figure 3 This is the structure diagram of the dataset EMPIAR-10304 based on the reference model EMD-10211, after multiple rounds of alignment-averaging iterations. Detailed Implementation
[0031] The technical solution of the present invention will be further described and illustrated below with reference to the embodiments.
[0032] Example 1
[0033] An adaptive filter-weighted sub-tomogram iterative alignment method, such as... Figure 1 As shown, the method includes the following steps: S1: Acquire cryo-electron microscopy tomographic image data and initial pose parameters, and perform data preprocessing; S2: Generate a list of Euler rotation angles within a given angle range and step size; S3: Adaptive filtering and weighting are applied to the processed sub-tomographic images and the reference template, and coarse alignment is performed: the cross-correlation matrix and translation parameters are calculated in the frequency domain space based on Fourier transform, and the Euler angle corresponding to the maximum cross-correlation value is selected as the optimal rotation angle. S4: Based on the Euler angles selected for coarse alignment, reduce the step size to generate a new Euler list, perform fine alignment, obtain the optimal rotation and translation parameters, and complete the alignment.
[0034] In one embodiment, the data preprocessing operation of S1 is specifically implemented according to the following steps: First, a dimensionality consistency check is performed on the input sub-tomographic images, initial reference model, and various masks. When dimensional inconsistencies are found, the smaller-dimensional 3D volumes are expanded to match the largest dimension using volume mean padding, ensuring dimensionality matching for all data in subsequent calculations.
[0035] Subsequently, the reference model centroid correction process is performed, such as... Figure 2As shown, the density is first preprocessed by removing noise through low-pass filtering, median filtering, and edge suppression, preserving the true signal. Then, a dynamic threshold is used to gradually expand from the high-density region, ensuring that the centroid calculation is based on the strong signal region. Finally, the centroid is calculated using the intersection of a binary reference mask and the core density region, avoiding interference from the solvent region, thus anchoring the centroid to the density region with the highest signal-to-noise ratio.
[0036] In one embodiment, in step S2, the generation of the Euler angle list is based on the input parameters. ,in Indicates the range of rotation outside the plane. For the corresponding step size, Indicates the range of rotation within the plane. This corresponds to the step size.
[0037] For each : ; For each ,generate : ; in: ; For each pair ,generate : ;
[0038] The final list of Euler angles is as follows: .
[0039] In one embodiment, in step S3, the rotation matrix R is calculated as follows: , ; in Represents a three-dimensional volume around The angle of rotation of the axis.
[0040] The rotation and translation involved the following four calculation methods: (1) Pure translation transformation: ; in: ; (2) Pure rotational transformation: ; in It's a data center offset. It is an inverse rotation matrix.
[0041] (3) First translate, then rotate: ; (4) Rotate first, then translate: .
[0042] In one embodiment, in S3, the adaptive bandpass filter, cRef(f), is calculated as follows: .
[0043] In one embodiment, the formula for calculating the frequency domain cross-correlation matrix in step S3 is as follows: ; in, Represents a three-dimensional sub-tomogram. Represents the reference model. The wedge mask representing the sub-tomogram. The wedge mask representing the reference model. This represents the inverse Fourier transform. This indicates taking the real part of a complex number.
[0044] In one embodiment, in step S3, the translation parameter is calculated as follows: first, the cross-correlation matrix is masked and filtered: ;
[0045] Detect the initial peak position: ;
[0046] The centroid is corrected, and a local window is defined with (maxX, maxY, maxZ) as the center and a radius peakCOM = 3. ;
[0047] Calculate the centroid offset: ; .
[0048] Update peak coordinates: ; The centroid is corrected twice: first using the original coordinates, and then using rounded integer coordinates to improve stability. The final translation parameters are: .
[0049] In one embodiment, the global cross-correlation value is calculated in step S3 as follows: ;
[0050] in, Represents a three-dimensional sub-tomogram. Represents the reference model. The wedge mask representing the sub-tomogram. The wedge mask representing the reference model. Indicates Fourier transform, This indicates taking the real part of a complex number.
[0051] Example 2
[0052] Based on Example 1, specific experimental verification was conducted. The publicly available cryo-electron microscopy tomography dataset EMPIAR-10304 was selected as the experimental verification data, and its corresponding high-quality reference structure EMD-10211 was used as the initial reference model. The dataset contains a large number of randomly oriented sub-tomographic particles with low signal-to-noise ratios, exhibiting a significant missing wedge effect, which can comprehensively verify the alignment stability and accuracy of the method of the present invention under complex real-world data conditions.
[0053] Figure 3 The figure shows the three-dimensional average structure obtained after multiple rounds of iterative convergence. As can be seen from the figure, the overall structure has a clear outline and continuous density distribution, with no obvious directional artifacts, indicating that the method of this invention can effectively suppress the anisotropic effects caused by missing wedges. Furthermore, the structure has rich surface details and a reasonable distribution of internal density regions, demonstrating that stable and reliable high-precision alignment can still be achieved under low signal-to-noise ratio conditions.
[0054] Furthermore, the gold-standard Fourier shell correlation (FSC) method was used to evaluate the resolution of the final reconstruction result, and the overall resolution at the FSC=0.143 criterion was calculated to be approximately 7.02 Å. This result is comparable to or better than that of existing similar methods on the same dataset, fully verifying that the parallel sub-tomogram alignment method proposed in this invention has significant advantages in both computational efficiency and reconstruction accuracy.
[0055] Based on the above embodiments, the present invention continues to describe in detail the technical features involved therein and the functions and roles of these technical features in the present invention, so as to help those skilled in the art to fully understand the technical solution of the present invention and reproduce it.
[0056] Finally, although this specification describes embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.
Claims
1. An adaptively filtered and weighted sub-tomographic map iterative alignment method, characterized in that, Includes the following steps: S1: Acquire cryo-electron microscopy tomographic image data and initial pose parameters, and perform data preprocessing; S2: Generate a list of Euler rotation angles within a given angle range and step size; S3: Adaptive filtering and weighting are applied to the preprocessed sub-tomographic images and the reference model, and coarse alignment is performed: the cross-correlation matrix and translation parameters are calculated in the frequency domain space based on Fourier transform, and the Euler angle corresponding to the maximum cross-correlation value is selected as the optimal rotation angle. S4: Based on the coarsely aligned Euler angles, reduce the step size to generate a new Euler list; S5: Perform fine alignment under the new Euler list to obtain the optimal rotation and translation parameters, and complete the alignment.
2. The sub-tomogram iterative alignment method as described in claim 1, characterized in that, S1 includes: S1-1: First, perform dimensionality checks on the input sub-tomographic images, reference models, various masks, and other data, and fill the smaller-dimensional 3D volumes into larger dimensions to ensure consistent dimensionality. S1-2: Centroid correction process based on high signal-to-noise ratio density region for the reference model; First, low-pass filtering and median filtering are applied to the reference model; Then, a dynamic thresholding method is used to generate a binary mask starting from the core density region with the highest signal-to-noise ratio through iterative expansion, ensuring that the centroid calculation is based only on the strong signal region and avoiding solvent noise interference; Finally, the weighted average spatial position of the density values within the high-confidence mask is calculated as the corrected centroid; Before comparison, the centroid is aligned with the geometric center of the sub-tomogram to eliminate initial bias.
3. The sub-tomogram iterative alignment method as described in claim 1, characterized in that, In step S2, the generation of the Euler rotation angle list depends on four parameters. ,in Indicates the range of rotation outside the plane. For the corresponding step size, Indicates the range of rotation within the plane. For the corresponding step size; For each : ； For each ,generate : ； in: ； For each pair ,generate : ； The final list of Euler angles is as follows: 。 4. The sub-tomogram iterative alignment method as described in claim 1, characterized in that, In step S3, the coarse alignment calculation process involves rotation and translation of the three-dimensional volume. Here, the rotation of sub-particles is performed using a ZXZ sequence, and trilinear interpolation is used to calculate the three-dimensional volume after rotation and translation. The rotation matrix R is calculated as follows: ； ； in Represents a three-dimensional volume around The angle of rotation of the axis.
5. The sub-tomogram iterative alignment method as described in claim 1, characterized in that, The rotation and translation calculations include: (1) Pure translation transformation: ； in: ； (2) Pure rotational transformation: ； in It's a data center offset. It is an inverse rotation matrix; (3) First translate, then rotate: ； (4) Rotate first, then translate: 。 6. The sub-tomogram iterative alignment method as described in claim 1, characterized in that, In S3, an adaptive bandpass filter is applied to the sub-tomographic image. The systematic process of this filter includes the original frequency coordinates, the original FSC value, the target frequency coordinates, and the forced mask vector as an artificial constraint. First, the original FSC value is processed to be non-negative. Then, the processed FSC curve is mapped to the target frequency coordinates by cubic spline interpolation. This process uses a clamping function to ensure that the interpolation operation is safely performed within the frequency range of the original data, thereby generating a smooth fitted FSC curve. Subsequently, an MTF correction model is introduced, which describes the detector's modulation transfer function in exponential form to compensate for the frequency response attenuation of the imaging system. Finally, the results of the preceding steps are integrated: the fitted FSC value is mathematically transformed into an FSC weight term, which is then multiplied by the MTF correction factor and the artificial constraint represented by the forced mask to obtain the final filter cRef(f); that is: 。 7. The sub-tomogram iterative alignment method as described in claim 1, characterized in that, In S3, the specific formula for calculating the cross-correlation matrix in the frequency domain is as follows: ； in, Represents a three-dimensional sub-tomogram. Represents the reference model. The wedge mask representing the sub-tomogram. The wedge mask representing the reference model. This represents the inverse Fourier transform. This indicates taking the real part of a complex number.
8. The sub-tomogram iterative alignment method as described in claim 1, characterized in that, The translation parameters are calculated as follows, and the cross-correlation matrix is used for masking filtering: ； Detect the initial peak position: ； The centroid is corrected, and a local window is defined with (maxX, maxY, maxZ) as the center and a radius peakCOM = 3. ； Calculate the centroid offset: ； ； Update peak coordinates: ； The centroid is corrected twice: first using the original coordinates, and then using rounded integer coordinates to improve stability; the final translation parameters are: 。 9. The sub-tomogram iterative alignment method as described in claim 1, characterized in that, The global cross-correlation value is calculated in the following specific steps: ； in, Represents a three-dimensional sub-tomogram. Represents the reference model. The wedge mask representing the sub-tomogram. The wedge mask representing the reference model. Indicates Fourier transform, This indicates taking the real part of a complex number.