Super-resolution particle fusion method based on deep learning point cloud registration

Abstract

The invention discloses a super-resolution particle fusion method based on deep learning point cloud registration, and belongs to the field of biological super-resolution microscopic imaging. According to the method, coarse particle alignment is carried out through deep learning, global alignment of particles with different orientations in a three-dimensional space is realized, the problem of a local optimal solution is avoided, and the final particle fusion reconstruction resolution is remarkably improved. Through an iterative coarse alignment mechanism, information of all particles is reasonably utilized, and the influence of initial template deviation is avoided. A loss function based on Gaussian distance is used, specific positioning uncertainty characteristics of SMLM data are introduced, and a deep learning point cloud registration network for SMLM biomacromolecule point cloud data is trained; and the precision and efficiency of super-resolution particle fusion are improved by using a deep learning point cloud registration network. And a simulation data set is constructed through system deployment of related parameters for network training, so that the generalization of the network is improved. A pre-training network is used to realize a particle fusion coarse alignment step, and the super-resolution particle fusion speed is accelerated.

Description

TECHNICAL FIELD

[0001] The present application relates to a particle fusion method based on deep learning point cloud registration, belonging to the technical field of biological super-resolution microscopic imaging. BACKGROUND

[0002] Single molecule localization microscopy (SMLM) is a breakthrough super-resolution imaging method, which can realize the visualization of biological structure at the molecular scale by accurately detecting and locating the sparsely activated fluorescent molecules. This technology provides nanoscale structural analysis capability for biomedical research. However, in practical application, the lack of fluorescent labeling density and single molecule localization error limit the further improvement of the resolution of SMLM. In order to further improve the resolution, researchers have developed particle fusion technology in the field of SMLM. This technology integrates the localization information of multiple particles in different orientations to obtain a complete structure average template, thereby improving the resolution. Ultimately, it can perform high-precision structural analysis on biological macromolecular data, providing a research tool for studying the spatial conformation and dynamic regulation of supramolecular assemblies.

[0003] Existing particle fusion algorithms such as the All-to-All method and the LocMoFit method directly act on the point cloud data of SMLM imaging, and obtain the optimal rigid transformation matrix by optimizing the distance between multiple particle point cloud data. The All-to-All method performs pairwise registration of each particle with all other particles, generates a similarity measure by optimizing the Bhattacharyya distance between the point pairs, and then uses Lie algebra decomposition to calculate all possible absolute positions and directions of each particle. Based on this, the particles are rotated and translated to obtain a data-driven initial template. Further alignment optimization is performed based on the template to obtain the final particle fusion reconstruction result. The LocMoFit method obtains the optimal transformation matrix between particles by optimizing the Gaussian distance between particle point cloud data, judges the similarity between particles according to the size of the Gaussian distance by performing pairwise registration on part of the particles, sorts the particles according to the similarity, and aligns and accumulates the particles in turn to obtain a data-driven initial template. Based on this initial template, all particles are aligned with it and the template is iteratively updated to ultimately obtain the particle fusion reconstruction result.

[0004] Existing methods can obtain a complete and clearer imaging reconstruction result on biological macromolecular data, but still have some problems. The traditional optimization algorithm is used to obtain the transformation relationship between particles, which makes it easy to fall into a local optimal solution when dealing with three-dimensional particle fusion tasks, especially for data sets with large initial rotation deviation. This limits the resolution of the final reconstruction result in the three-dimensional global space particle fusion task, and accurate biological macromolecular structure information cannot be observed. Summary of the Invention

[0005] To address the issue of insufficient resolution in existing methods for 3D particle fusion applications, the present invention aims to provide a super-resolution particle fusion method based on deep learning point cloud registration, employing the DeepFusion framework, which can improve the resolution of biomacromolecules in 3D particle fusion tasks.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The super-resolution particle fusion method DeepFusion based on deep learning point cloud registration disclosed in this invention includes the following steps:

[0008] Step 1: Particle Fusion Data Input and Preprocessing: The SMLM imaging data is segmented to obtain N individual particles, which are then combined into a dataset. Each particle is defined as P = {p1, p2, ..., p...}. i ,...,p n It consists of n three-dimensional points, each point p i =(x i ,y i ,z i ,∑ i Includes spatial coordinates And the positioning uncertainty of SMLM data ∑ i .

[0009] Step 2: Gaussian Mixture Model Modeling: Use the pre-trained neural network model to model the dataset from Step 1, predicting the Gaussian Mixture Model (GMM) for each particle, thereby obtaining the set of GMMs corresponding to the dataset. Each GMM can be represented as α j For mixed weights, The mean is μ j Covariance is The distribution is Gaussian, and J is the number of Gaussian models in the GMM.

[0010] Step 3: Coarse alignment based on Gaussian mixture model: Perform rotation and translation transformation on the particles according to the predicted particle GMM model.

[0011] Step 3.1: Initial Coarse Alignment Transformation: Randomly select the GMM of one particle as the target model, and the corresponding point cloud data is the target point cloud. Use the GMMs of the remaining particles to be aligned as source models, and the corresponding point cloud data is the source point cloud. Solve the transformation matrix from each source model to the target model using the rotation and translation matrix calculation module.

[0012] Step 3.2: Update the coarse alignment template and solve the transformation: Use the transformation matrix obtained in the previous step to transform the source model to obtain the transformed source model, and then superimpose the transformed source models to generate a new target model. Repeat the transformation matrix solving process in Step 3.1 to obtain a new transformation matrix.

[0013] Step 3.3: Iterative Coarse Alignment Transformation: Repeat the process in Step 3.2 to obtain the final transformation matrix. Apply the corresponding transformation matrix to each source point cloud for spatial transformation to obtain the coarsely aligned dataset. Superimpose all the coarsely aligned data to obtain the coarsely aligned particle fusion result.

[0014] Step 4: Fine Alignment Optimization:

[0015] Single-molecule localization imaging suffers from localization errors, missing sites, and noise interference, leading to significant differences in the Gross Model (GMM) features of individual particles. Although deep learning networks can predict GMM parameters and achieve globally optimal registration, avoiding local optima, the alignment results directly output still contain biases due to noise and model limitations. Therefore, the network output is used as a coarse alignment result to provide high-quality initial values ​​for subsequent fine alignment. The fine alignment step corrects residual errors, significantly improving the final alignment accuracy.

[0016] Step 4.1: Initial Fine Alignment Optimization: Using the coarse alignment particle fusion result obtained in Step 3 as the data-driven template, the coarse-aligned dataset is further fine-aligned with the data-driven template. Fine alignment is achieved by optimizing the Gaussian distance to obtain the fine alignment transformation matrix. The fine alignment transformation matrix is ​​then used to transform the coarse-aligned dataset, and the transformation results are superimposed to obtain a new data-driven template, which is then updated.

[0017] Step 4.2: Iterative fine alignment optimization: Repeat step 4.1 iteratively to obtain the final fine alignment transformation matrix. Transform the dataset after coarse alignment to obtain the fine alignment dataset. Then, stack the fine alignment datasets together to obtain the final particle fusion result.

[0018] Furthermore, the specific method for training the network of the pre-trained model in step 2, Gaussian mixture modeling, is as follows:

[0019] Step 2.1: Constructing the Training Dataset: The quality of single-molecule localization imaging is mainly determined by key parameters such as label density (DOL), localization uncertainty (LU), and localization quantity per site (LPS). These parameters directly affect the imaging resolution and the accuracy of structure reconstruction. This invention uses simulated data to comprehensively adjust these parameters, generating datasets with different imaging qualities for network training.

[0020] Step 2.1.1: Design real marker site structures based on real biological macromolecular structural information.

[0021] Step 2.1.2: Generate an initial model based on the biomacromolecule particle structure information designed in Step 2.1.1.

[0022] Step 2.1.3: Simulate site loss in SMLM imaging data. Sites are removed from the initial model according to the set DOL parameters, resulting in a model with sites removed.

[0023] Step 2.1.4: Simulate the number of localization points. The distribution of the number of localization points corresponding to each marked site follows a Poisson distribution. Based on this assumption, according to the set LPS parameters, a random number conforming to a Poisson distribution is generated for each site in the model after the sites have been removed. This random number represents the final number of localization points at that site. The point cloud data of each site is expanded by adding a corresponding number of points based on the random numbers, thereby obtaining simulated particles that simulate the number of localization sites.

[0024] Step 2.1.5: Perform random rotation and translation operations on the simulated particles with the simulated number of positioning sites to simulate the random orientation of biomolecular structures in three-dimensional space. Based on pre-set upper and lower bounds for the rotation angle and translation scale, perform rotation and translation transformations on the simulated particles with the simulated number of positioning sites along the x, y, and z axes to obtain the rotated simulated particles. The rotation operation is achieved by generating random rotation angles within a range and applying a three-dimensional rotation matrix. The translation operation is achieved by generating random translation amounts along the three axes to move the entire data to a new spatial position.

[0025] Step 2.1.6: Add a LU (Local Allocation) parameter to the rotated simulated particle to simulate the positioning error caused by optical system noise and molecular scintillation characteristics in SMLM imaging. The LU is set to a fixed value, and it is assumed that the LU is consistent in the xy-plane and z-axis directions. In real imaging, the LU causes the positioning points to form clusters around the real sites; in the simulation, it is assumed that the distribution of these clusters follows a Gaussian distribution. Based on this assumption, for each point in the rotated simulated particle, a standard normally distributed random number is generated in both the xy-plane and z-axis directions, and then multiplied by the LU parameter value to obtain the offset in that direction. Next, to further enhance the diversity and uniformity of the data and avoid generating a large number of duplicate values, an additional random number between 0 and 1 is added to the offset as a fine-tuning step, resulting in a new offset. Each point is offset based on its offset to obtain the final simulated particle.

[0026] Step 2.1.7: Set different DOL, LU and LPS parameters, and repeat steps 2.1.2 to 2.1.6 above to generate multiple simulated particles to form a training set.

[0027] Step 2.2: Training Data Preprocessing: After preprocessing the training set data, each pair of particles is used as an input pair, with one particle serving as the target particle and the other as the source particle to be aligned. This yields the preprocessed training set.

[0028] Step 2.3: Network Training: Input the preprocessed granular data from the training set into the network in pairs to train the network, and at the same time construct a loss function to evaluate the model's prediction performance.

[0029] For the input particle data, there is a positioning uncertainty (σ). x ,σ y ,σ z This means that each location point in the particle data does not represent the actual site of the molecule, but is approximately distributed around the actual location in a Gaussian distribution. In other words, each actual site is represented as a location with uncertainty (σ) centered on the actual site. x ,σ y ,σ z The standard deviation is denoted as 3D Gaussian point cloud distribution. Based on this characteristic, the distance between two particle point cloud data can be quantified using a Gaussian function. For a localization point in the source particle... The likelihood between the point cloud and the target particle can be described by a Gaussian function. This likelihood description considers not only the spatial location of the localization point but also the localization uncertainty, thus more accurately reflecting the matching relationship between point clouds. The likelihood function can be expressed as:

[0030]

[0031] in, This represents a location point within the source particle. Let n represent the i-th positioning point in the target particle. tgt This indicates the total number of target particle positioning points. It is a diagonal matrix representing the squared uncertainty of the source point cloud localization, and det(∑) is its determinant, where ∑ represents isotropy, i.e., σ x =σ y =σ z T = f θ (·) is the output of the network, representing the parameters of the rigid transformation, including the rotation matrix and translation vector.

[0032] For each point in the source particle, treated as an independent event, the likelihood function can be expressed as the product of individual likelihood functions for all localization points in the entire particle:

[0033]

[0034] Where n srcThis represents the number of localization points in the source particle. To simplify the calculation and avoid numerical instability caused by multiple multiplications, we take the log-likelihood of the likelihood function, obtaining:

[0035]

[0036] A higher value for the log-likelihood function indicates a better match between the source and target particle point clouds. However, neural network optimization typically aims to minimize the loss function. Therefore, to align with the optimization framework, we further take the negative logarithm of the log-likelihood function to obtain the final loss function:

[0037]

[0038] By minimizing this loss function, the network parameters can be optimized so that the transformation parameters T = f of the network output. θ (·) This design maximizes the matching degree between the source and target particle point clouds. This not only aligns with the optimization objectives of neural networks but also improves optimization efficiency by increasing gradients.

[0039] Step 2.4: Repeat step 2.3 above until the number of iterations reaches the target number of iterations determined by the environmental parameters in the model building stage, and the model performance evaluation given by the above loss function is close to stable between training rounds and no longer shows significant improvement. The significant improvement refers to the improvement range not exceeding the preset threshold.

[0040] Step 2.5: Save the model parameters for use by the particle fusion method.

[0041] Furthermore, in step 2, the dataset preprocessing part of the pre-trained model's network training in Gaussian mixture modeling involves the following processing:

[0042] ① Normalize all particle data (scale the coordinate values ​​to the [-1,1] interval) to eliminate the impact of scale differences on network training and obtain the normalized training set.

[0043] ② To enhance the generalization ability of the model, a data augmentation strategy is adopted. Q source particles are randomly selected for each target particle, generating a total of N×Q training sample pairs. Random rotation transformation is applied to each pair of samples to enrich the diversity of spatial orientation, resulting in a data-augmented training set.

[0044] ③ For the input particle data, it is necessary to ensure that the length of the point cloud data in the same batch is consistent. A sampling and filling strategy is adopted to expand each point cloud data to the maximum length of the batch. The filling points are generated according to the positioning uncertainty parameters of the original data to obtain the final preprocessed training set.

[0045] Beneficial effects:

[0046] 1. The super-resolution particle fusion method based on deep learning point cloud registration disclosed in this invention uses deep learning to perform coarse alignment of particles, achieving global alignment of particles with different orientations in three-dimensional space, avoiding the problem of local optima, and significantly improving the resolution of the final particle fusion reconstruction.

[0047] 2. The super-resolution particle fusion method based on deep learning point cloud registration disclosed in this invention makes reasonable use of the information of all particles through an iterative coarse alignment mechanism, avoiding the influence of initial template bias.

[0048] 3. The super-resolution particle fusion method based on deep learning point cloud registration disclosed in this invention introduces the localization uncertainty feature unique to SMLM data by using a loss function based on Gaussian distance, and trains a deep learning point cloud registration network for SMLM biological macromolecular point cloud data; the deep learning point cloud registration network is used to improve the accuracy and efficiency of super-resolution particle fusion.

[0049] 4. The super-resolution particle fusion method based on deep learning point cloud registration disclosed in this invention constructs a simulated dataset for network training by systematically adjusting relevant parameters, thereby improving the generalization of the network.

[0050] 5. The super-resolution particle fusion method based on deep learning point cloud registration disclosed in this invention uses a pre-trained network to implement the coarse alignment step of particle fusion, which significantly improves computational efficiency and accelerates the super-resolution particle fusion speed. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the DeepFusion super-resolution particle fusion method based on deep learning point cloud registration according to the present invention.

[0052] Figure 2 This is a schematic diagram of the simulated data structure of the training set during network training in this invention.

[0053] Figure 3 This is a schematic diagram of simulated data constructed during network training in this invention.

[0054] Figure 4 This is a diagram of a deep learning network structure provided in an embodiment of the present invention.

[0055] Figure 5 This invention is applied to real data of nuclear pore complex (NPC) structures. Figure a shows the reconstruction result of particle fusion using the DeepFusion method after rotation processing, showing the top view, side view, and top view of the upper and lower rings. Figure b shows the NPC structure analysis after particle fusion reconstruction with high-angle initial rotation. Figures c and d show the NPC particle fusion results and structure analysis without rotation processing. Detailed Implementation

[0056] The present invention will now be described in detail with reference to the accompanying drawings. However, it should be understood that the drawings are provided only to better understand the present invention and should not be construed as limiting the present invention.

[0057] The super-resolution particle fusion method (DeepFusion) based on deep learning point cloud registration in this embodiment can further improve the resolution of SMLM microscopy imaging. The specific implementation steps are as follows:

[0058] Step 1: Network training of the pre-trained model: This step is not necessary if a pre-trained network model has already been prepared.

[0059] Step 1.1: Design the structure of the simulation data based on the actual biological macromolecular structure, such as... Figure 2 The four designed NPC structures consist of 16 sites. Based on these four structures, site removal was first performed to simulate the absence of labeled sites in real SMLM imaging. For each structure, the DOL was set to 70%, meaning 11 out of the 16 sites were labeled. All combinations of the 11 sites were iterated, generating 4368 different site combinations for each structure, covering all possible site loss scenarios. Secondly, the scintillation of localization points was simulated, with LPS set to 5, assuming a Poisson distribution, to simulate fluctuations in the number of localization points caused by molecular scintillation characteristics. Finally, bias caused by localization uncertainty was simulated. To enhance the diversity of the training data, the LU was set to a mixed range, meaning the LU of each particle remained consistent within the particle but was randomly sampled from [2 nm, 4 nm, 6 nm, 8 nm, 10 nm] between different particles. This design allows the training data to cover localization point distributions under various different LUs, thereby improving the network's adaptability and robustness to different imaging conditions. Furthermore, the rotation angle range was set to ±180° to fully simulate the random orientation of the nuclear-pore complex in three-dimensional space. The final generated simulation data looks like this Figure 2 As shown, the simulation results are presented under different LU and DOL parameters in the Nup107 structure.

[0060] Step 1.2: Based on the structure and parameter settings designed in Step 1.1, simulate and generate the NPC structure training dataset. There are 4 groups, each corresponding to one structure and containing 4368 particles. Each particle P = {p1, p2, ..., p...} i ,...,p n It consists of n three-dimensional points, each point p i =(x i ,y i ,z i ,∑ iIncludes spatial coordinates And the positioning uncertainty of SMLM data ∑ i .

[0061] Step 1.3: Construct a neural network using deep learning to train the deep learning-based SMLM point cloud data registration network. Set the appropriate hyperparameters, including the network learning rate of 0.0001 and batch size of 16. The DeepGMR network is selected as the deep learning network, and its structure is as follows... Figure 3 As shown.

[0062] Step 1.4: Data Preprocessing. First, all particle data is normalized (coordinate values ​​are scaled to the [-1,1] interval) to eliminate the impact of scale differences on network training. To enhance the model's generalization ability, a data augmentation strategy is adopted. For each target particle, 100 source particles are randomly selected, generating N×100 training sample pairs. A random rotation transformation is applied to each sample pair to enrich the diversity of spatial orientation. Finally, to ensure consistent length of point cloud data within the same batch, a sampling and padding strategy is used to expand each point cloud data to the maximum length of the batch. The padding points are generated based on the localization uncertainty parameters of the original data, using the same method as simulating localization uncertainty in Step 1.1. This processing method not only ensures the dimensional consistency of the input data but also guarantees that the supplementary data strictly follows the statistical distribution characteristics of the original data, thus effectively maintaining the consistency between the structural information represented by the point cloud data and the original data.

[0063] Step 1.5: Train the network by backpropagating the model parameters using the loss function to ensure the model correctly understands the structural information of the particles. The loss function is set to...

[0064]

[0065] in, This represents a location point within the source particle. Let n represent the i-th positioning point in the target particle. tgt This represents the total number of target particle positioning points. src This indicates the total number of target particle positioning points. It is a diagonal matrix representing the squared uncertainty of the source point cloud localization, and det(∑) is its determinant. Here, we assume that ∑ is isotropic, i.e., σ x =σ y =σ z T = f θ (·) is the output of the network, representing the parameters of the rigid transformation, including the rotation matrix and translation vector.

[0066] Step 1.6: Repeat the above steps until the number of iterations reaches the target number determined in the model building phase, and the model performance evaluation given by the above loss function is nearly stable between training epochs, no longer showing significant improvement. The pre-trained network model is then obtained.

[0067] Step 2: Application of the DeepFusion particle fusion method. For example... Figure 1 As shown, the implementation process of the particle fusion method of the present invention is as follows.

[0068] Step 2.1: Preprocess the input data by dividing the input SMLM data into a dataset consisting of N individual particles.

[0069] Step 2.2: Input the dataset into the pre-trained network from Step 1 to predict the GMM for each particle. Obtain the set of GMMs corresponding to the dataset.

[0070] Step 2.3: Randomly select one particle from the dataset as the target particle, and its corresponding GMM is the target model. The remaining particles are source particles, and their corresponding GMMs are source models. Solve the transformation matrices from each source model to the target model using the rotation and translation matrix calculation module to obtain the set of transformation matrices. The rotation and translation matrix calculation module is implemented using weighted singular value decomposition.

[0071] Step 2.4: Transform the source model using the transformation matrix set and then fuse the transformed source model. First, filtering is performed based on the set threshold conditions (maximum eigenvalue of the covariance matrix and weight threshold) to remove noise and minor components. Then, the components that pass the validity test are weighted and averaged for fusion. The fusion weight is the sum of the weights of each valid component, while the mean and covariance matrix are calculated according to their respective weights. After fusion, a new target model is obtained and updated. The transformation matrix solution process in Step 2.3 is repeated, and the bias caused by the initial template selection is reduced through iterative optimization to obtain the final transformation matrix set.

[0072] Step 2.5: Based on the final set of transformation matrices, apply corresponding rigid transformations to the point cloud data of each source particle to obtain the coarsely aligned dataset. Superimpose the coarsely aligned datasets to obtain the coarsely aligned particle fusion result.

[0073] Step 2.6: Using the coarse-aligned particle fusion result as a data-driven template, the coarse-aligned dataset is then fine-aligned again with this template. The fine-alignment step calculates the optimal rotation and translation matrix by optimizing the Gaussian distance. Fine-alignment iteratively improves the alignment accuracy between each particle and the data-driven template. In each iteration, for each particle P in the dataset... i From data-driven templates Remove current particle P from the middlei Obtain the target point cloud and P i As the source point cloud As the target point cloud, optimize the transformation parameter T. i =(R i ,t i To minimize the cost function, which is defined as the source point cloud P i With target point cloud The Gaussian distance between them. During the optimization process, a gradient-based optimization algorithm is used to minimize the cost function, and the gradient is calculated and the transformation parameters T are updated in each iteration. i The optimization process terminates when the change in the cost function is less than a preset threshold or when the maximum number of iterations is reached, and the particle size P is updated. i The position is R i P i +t i Finally, a fine alignment transformation matrix is ​​obtained. This fine alignment transformation matrix is ​​used to transform the coarsely aligned dataset, and the transformation results are superimposed to obtain a new data-driven template, which is then updated.

[0074] Step 2.7: Iterative fine alignment optimization: Repeat step 2.6 iteratively to obtain the final fine alignment transformation matrix, transform the dataset after coarse alignment transformation, and superimpose them to obtain the final particle fusion result.

[0075] Figure 4 This paper presents the application results of the particle fusion reconstruction method of the present invention on real Nup96 structure SMLM imaging data. It compares the reconstruction results of 500 particles in their original state and after adding random rotation. The experimental data with added random rotation applied random rotations within ±180° along the x, y, and z axes. Analysis of the reconstruction results in the xy and xz planes for both rotation conditions shows that the characteristic double-ring structure of the NPC was successfully reconstructed under both conditions, and each ring clearly exhibits an eight-fold symmetric subunit distribution with spatial separation characteristics. The results demonstrate that the DeepFusion method has excellent processing capabilities for high-angle rotation (full-space random orientation) datasets, and its reconstruction effect remains highly consistent with that of low-angle (original, unrotated) datasets, verifying the robustness of the method of the present invention in three-dimensional spatial particle fusion reconstruction tasks.

[0076] A systematic analysis was performed on two sets of reconstructed Nup96 structures: one with rotated data (±180° high-angle data) and the other without rotation (low-angle data). Three key structural parameters of the nucleopore complex were determined: the interloop spacing (Δz), the upper and lower loop radii (r1, r2), and the deviation angle between the interloops. The results show that the final measured distance between the two rings from the high-angle data is 47.3 nm, with upper and lower ring radii of 53.8 nm and 53.4 nm, respectively, and a deviation angle of 7.7°. The corresponding results from the low-angle data reconstruction are 47.8 nm, 54.3 nm, 52.7 nm, and 8.2°.

[0077] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A super-resolution particle fusion method based on deep learning point cloud registration, characterized in that: Includes the following steps: Step 1: Particle fusion data input and preprocessing: Segment the SMLM imaging data to obtain N individual particles, and combine these N particles into a dataset; Step 2: Gaussian Mixture Model Modeling: Construct a training dataset, pre-train a neural network model using the training dataset, and then use the neural network model to model the dataset from Step 1, predicting the Gaussian Mixture Model (GMM) for each particle, thereby obtaining the set of GMMs corresponding to the dataset. Step 3: Perform rotation and translation transformations on the particles based on the GMM model predicted in Step 2 to achieve coarse alignment; Step 4: Transform the dataset after coarse alignment transformation in Step 3 to obtain fine alignment dataset. Superimpose the fine alignment datasets to obtain the final particle fusion result.

2. The super-resolution particle fusion method based on deep learning point cloud registration as described in claim 1, characterized in that: Step 1: Each particle in the dataset is P = {p1, p2, ..., p...} i ...,p n It consists of n three-dimensional points, each point p i =(x i ,y i ,z i ,∑ i Includes spatial coordinates And the localization uncertainty of single-molecule localization data ∑ i .

3. The super-resolution particle fusion method based on deep learning point cloud registration as described in claim 1, characterized in that: Each GMM in step 2 is represented as α j For mixed weights, The mean is μ j Covariance is The distribution is Gaussian, and J is the number of Gaussian models in the GMM.

4. The super-resolution particle fusion method based on deep learning point cloud registration as described in claim 1, characterized in that: The specific implementation method of step 3 is as follows: Step 3.1: Initial coarse alignment transformation: Randomly select the GMM of one particle as the target model, and the corresponding point cloud data is the target point cloud; take the GMMs of the remaining particles to be aligned as the source models, and the corresponding point cloud data is the source point cloud; solve the transformation matrix from each source model to the target model through the rotation and translation matrix calculation module. Step 3.2: Update the coarse alignment template and solve the transformation: Use the transformation matrix obtained in the previous step to transform the source model to obtain the transformed source model, and superimpose the transformed source models to generate a new target model; repeat the transformation matrix solving process in Step 3.1 to obtain a new transformation matrix; Step 3.3: Iterative coarse alignment transformation: Repeat the process of step 3.2 to obtain the final transformation matrix; apply the corresponding final transformation matrix to each source point cloud to perform spatial transformation to obtain the dataset after coarse alignment transformation; By superimposing all the data after coarse alignment transformation, the coarse alignment particle fusion result is obtained.

5. The super-resolution particle fusion method based on deep learning point cloud registration as described in claim 1, characterized in that: The specific implementation method of step 4 is as follows: Step 4.1: Initial fine alignment optimization: Using the coarse alignment particle fusion result obtained in Step 3 as the data-driven template, the dataset after coarse alignment transformation is further finely aligned with the data-driven template; Fine alignment is achieved by optimizing the Gaussian distance calculation to obtain the fine alignment transformation matrix; The dataset after coarse alignment transformation is transformed using a fine alignment transformation matrix, and the transformation results are superimposed to obtain a new data-driven template, which is then updated. Step 4.2: Iterative fine alignment optimization: Repeat step 4.1 iteratively to obtain the final fine alignment transformation matrix. Transform the dataset after coarse alignment to obtain the fine alignment dataset. Then, stack the fine alignment datasets together to obtain the final particle fusion result.

6. The super-resolution particle fusion method based on deep learning point cloud registration as described in claim 1, characterized in that: Step 2 involves constructing the training dataset as follows: Step 2.1: Design real marker site structures based on real biological macromolecular structure information; Step 2.2: Generate an initial model based on the site structure from Step 2.1; Step 2.3: Remove sites from the initial model according to the preset DOL parameters to obtain a model with sites removed; Step 2.4: Based on the preset LPS parameters, generate a random number conforming to a Poisson distribution for each site in the model where sites have been removed. This random number represents the final number of locations at that site. Expand the point cloud data of each site by adding a corresponding number of points based on the random number to obtain simulated particle A. The simulated particle A simulates the number of locations. Step 2.5: Based on the pre-set upper and lower bounds of the rotation angle and translation scale, perform rotation and translation transformations on the simulated particle A along the x, y, and z axes respectively to obtain the rotated simulated particle B; Step 2.6: For each point in the simulated particle B, first generate a random number with a standard normal distribution in the xy plane and z-axis direction respectively, and then multiply it by the preset LU parameter value to obtain the offset in that direction; then, add an additional random number between 0 and 1 to the offset as fine-tuning to obtain a new offset. Each point is offset based on its offset value to obtain the final simulated particle C; Step 2.7: Set different DOL, LU and LPS parameters, and repeat steps 2.2 to 2.6 above to generate multiple simulated particles to form a training dataset.

7. The super-resolution particle fusion method based on deep learning point cloud registration as described in claim 1, characterized in that: The specific method for network training of the pre-trained model in step 2 of Gaussian mixture modeling is as follows: Step 2.1: After preprocessing the training set data, the preprocessed training set is obtained; Step 2.2: Network Training: The granular data in the preprocessed training set is used to iteratively train the input neural network model. The difference between the model output and the true value is calculated in real time using the constructed loss function, and the model parameters are adjusted in reverse based on the difference. The above training process is repeated until the preset number of iterations is reached to obtain the pre-trained neural network model. The method for constructing the loss function is as follows: The distance between two particle point cloud data is quantized using a Gaussian function; for a localization point in the source particle... The likelihood between it and the target particle can be described by a Gaussian function; the likelihood function is expressed as: in, This represents a location point in the source particle; Let n represent the i-th positioning point in the target particle. tgt Indicates the total number of target particle positioning points; It is a diagonal matrix of the squared uncertainty of the source point cloud localization, and det(∑) is its determinant; T = f θ (·) is the output of the network, representing the parameters of the rigid transformation, including the rotation matrix and translation vector; For each point in the source particle, it is treated as an independent event. Therefore, for all localization points in the entire source particle, the likelihood function is expressed as the product of individual likelihood functions: Where n src This represents the number of location points in the source particle; to simplify the calculation and avoid numerical instability caused by multiplication, we take the log-likelihood of the likelihood function, resulting in: A larger value for the log-likelihood function indicates a higher degree of matching between the source and target particle point clouds. However, neural network optimization typically aims to minimize the loss function. Therefore, to align with the optimization framework, we further take the negative logarithm of the log-likelihood function to obtain the final loss function: By minimizing this loss function, the network parameters can be optimized so that the transformation parameters T = f of the network output. θ (·) can maximize the matching degree between the source particle point cloud and the target particle point cloud.

8. The super-resolution particle fusion method based on deep learning point cloud registration as described in claim 7, characterized in that: The rotation operation described in step 2.5 is achieved by generating a random rotation angle within a range and applying a three-dimensional rotation matrix; the translation operation is achieved by generating random translation amounts in three axes to move the data as a whole to a new spatial position.

9. The super-resolution particle fusion method based on deep learning point cloud registration as described in claim 8, characterized in that: The method for preprocessing the training set data is to normalize all granular data. A data augmentation strategy is adopted to randomly select Q source particles for each target particle, generating a total of N×Q training sample pairs, and applying random rotation transformation to each training sample pair to enrich the diversity of spatial orientation. Obtain the data-augmented training set; then pad the data-augmented training set to ensure that the length of point cloud data in the same batch is consistent; For the input particle data, it is necessary to ensure that the length of the point cloud data in the same batch is consistent. A sampling and filling strategy is adopted to expand each point cloud data to the maximum length of the batch. The filling points are generated based on the positioning uncertainty parameters of the original data.

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