Nested representation 3d reconstruction method based on dynamic gaussian framework

Abstract

This invention discloses a nested representation 3D reconstruction method based on a dynamic Gaussian framework, belonging to the field of 3D reconstruction technology. The method includes the following steps: acquiring a dynamic 3D data sequence of a dynamic 3D scene; constructing a temporal feature sequence; defining a dynamic kernel function and updating parameters; modeling and optimizing the dynamic Gaussian process; and deriving the posterior prediction distribution of the Gaussian process based on Bayesian inference. This invention achieves full-scale feature capture based on multi-scale nested features and adaptive weighted fusion of information entropy; designs a time-dependent dynamic kernel function to construct a Gaussian process probability model to complete accurate reconstruction inference; and achieves joint iterative optimization of feature weights and kernel parameters through closed-loop feedback of prediction errors. It combines the comprehensiveness of multi-scale features, the adaptability of dynamic modeling, and the robustness of closed-loop optimization, significantly improving the reconstruction accuracy and detail reproduction of dynamic 3D data. It is applicable to various scenarios such as dynamic point clouds and dynamic meshes, and has strong engineering practical value.

Description

Technical Field

[0001] This invention relates to the field of 3D reconstruction technology, and in particular to a 3D reconstruction method based on a nested representation of a dynamic Gaussian frame. Background Technology

[0002] A dynamic 3D scene refers to a virtual or digital twin scene that includes a 3D spatial structure, where objects and characters within the scene move (e.g., a person dancing, a robotic arm moving, a vehicle moving), or where the scene's shape and structure change over time (fluid flow, deformed objects, dynamic environment), and supports real-time interaction or evolution. The data for a 3D scene is point cloud or 3D mesh data.

[0003] In fields such as dynamic scene reconstruction, dynamic scene perception, and high-dimensional data modeling, traditional 3D reconstruction methods rely on single-scale feature extraction, which suffers from shortcomings such as one-sided feature representation, poor adaptability to dynamic data distribution, and insufficient modeling robustness. Nested representation learning, as a multi-granularity feature learning technique, can achieve hierarchical feature clipping and multi-scale information extraction, but when applied alone to 3D reconstruction, it cannot adapt to the temporal distribution changes of dynamic data, and the model's generalization ability is limited. On the other hand, the dynamic Gaussian processing framework has excellent dynamic probability modeling and data fitting capabilities, but it lacks multi-scale, fine-grained feature support, resulting in insufficient reconstruction accuracy and serious loss of details.

[0004] Therefore, existing related technologies have not achieved end-to-end fusion of nested representation and dynamic Gaussian framework. They lack both multi-scale nested feature adaptive weighting logic and dynamic Gaussian modeling process with real-time kernel parameter updates, and cannot solve the dual technical problems of "incomplete feature representation + insufficient dynamic adaptation" in dynamic 3D reconstruction.

[0005] Definitions: A Gaussian process (GP) is a nonparametric statistical model used for regression and classification. In a Gaussian process, the function value at any point is assumed to be a random variable, and these variables follow a joint Gaussian distribution. Once some points of the function have been observed, a Gaussian process can be used to predict the function values ​​at unobserved points.

[0006] Mean Squared Error (MSE) is the error caused by the mean squared squared error. Summary of the Invention

[0007] The purpose of this invention is to provide a nested representation 3D reconstruction method based on a dynamic Gaussian framework that solves the above problems, provides more comprehensive multi-scale feature representation, stronger dynamic modeling adaptability, and higher robustness of closed-loop optimization.

[0008] To achieve the above objectives, the technical solution adopted by this invention is as follows: a nested representation three-dimensional reconstruction method based on a dynamic Gaussian framework, comprising the following steps: S1, acquire the dynamic 3D data sequence X of the dynamic 3D scene and preprocess the dynamic 3D data sequence. In the formula, The original three-dimensional data x at time step t t The corresponding preprocessed data, where T is the total number of time steps; S2, construct the time-series feature sequence F. The multi-scale fusion feature F at time step t t The construction method includes steps S21 to S22; S21, will Mapping to a high-dimensional feature space yields the basic features. Then, the layers are further pruned into K nested features of different scales. The nested features at scale k are... The initial weights ω of features at each scale are calculated using the information entropy function. k , 1≤k≤K; S22, sort the K nested features by ω k Weighted fusion of multi-scale fusion features F at time step t t ; S3 defines the dynamic kernel function for time step t; , , In the formula, F i F j These are the multi-scale fusion features at time steps i and j, respectively. Let be the dynamic kernel function of the multi-scale fusion features at time step t over two time steps. Let l(t) be the signal variance at time step t, and l(t) be the length scale parameter of time step t. For Euclidean distance, Var(F) 1:t ) is F1~F t The sample variance The length of the sliding window. Let F represent the feature sequence obtained with two time steps as the two endpoints, where Med(⋅) is the median function, and the initial value of the signal variance is preset. =0.5, the initial value of the length scale parameter is l(0)=1; S4, Dynamic Gaussian process modeling and parameter optimization, including S41~S43; S41, Construct the time series covariance matrix K t K t element in row i and column j , For noise variance, The Kronecker function; S42, Define the output sequence of a Gaussian process. Prior distribution of Gaussian process GP(⋅,⋅) is a Gaussian process, m(F)=0 is the mean function, and y t The predicted three-dimensional data for time t; S43, ω k , Using l(0) as learnable parameters, gradient descent is used to minimize y and The MSE error is updated until the preset iteration stop condition is met; S5, Given a temporal feature sequence F, multi-scale fusion features for the time step to be predicted. Based on Bayesian inference, the posterior prediction distribution of the Gaussian process is derived, and the posterior mean is calculated. and posterior variance ,Will As the optimal estimate for the 3D reconstruction of the time step to be predicted.

[0009] As a preferred option, S1 is specifically: Obtain the raw 3D data of a dynamic 3D scene at continuous time steps, using the raw 3D data x at time step t. t Constructing dynamic three-dimensional data sequences ; For x t The Z-score standardization method is used to eliminate data dimensions, and then the 3σ principle is used to detect and remove outliers to obtain preprocessed data at time step t. This constitutes a preprocessed dynamic three-dimensional data sequence. ; As a preferred embodiment: S21 includes Sa1 to Sa3; Sa1, the basic features are obtained by mapping according to the following formula. , , In the formula, W0 and b0 are the weight matrix and bias during mapping, respectively. , , D and d0 respectively and The feature dimension, d0 > D; Sa2, with K preset feature dimensions, where the k-th feature dimension d k =α k d0, α∈(0,1) is the scale decay coefficient, in Before the cut Nested features of dimension k constituting scale k are ; Sa3, ω is calculated according to the following formula k : , In the formula, H(⋅) is the information entropy function, p kj This is the probability density of dimension j at scale k, calculated based on feature component normalization.

[0010] As a preferred option: S22 specifically involves: placing each Based on the trailing zero-padding method, map it to the basic feature dimension to obtain the corresponding padded features. Then, F is obtained by weighted fusion according to the formula. t , .

[0011] As a preferred option: in S43, the MSE error L MSE Calculate according to the following formula: .

[0012] Preferably, in S5, the Gaussian process posterior prediction distribution satisfy: , In the formula, , , , These represent the predicted 3D data for the time step to be predicted, multi-scale fusion features, posterior mean, and posterior variance, respectively. It follows a Gaussian distribution, and , Calculate according to the following formula: , .

[0013] As can be seen from the above scheme, this invention takes nested representation multi-scale feature extraction as its core, constructs a multi-level feature space from coarse to fine, and achieves full-scale feature capture through adaptive weighted fusion of information entropy; combined with an end-to-end dynamic Gaussian processing framework, it designs a time-dependent dynamic kernel function, updates kernel parameters in real time based on time-series feature statistics, and constructs a Gaussian process probability model to complete accurate reconstruction inference; through closed-loop feedback of prediction error, it achieves joint iterative optimization of feature weights and kernel parameters, thus forming a complete technical link of "feature extraction - dynamic modeling - error optimization". Specifically: 1. Regarding step S1: The treasure vault obtains a dynamic 3D data sequence X and preprocesses it into a dynamic 3D data sequence. Original 3D data The preprocessing includes Z-score normalization and 3σ principle detection. Z-score normalization eliminates differences in data dimensions, unifies the global data distribution, and prevents modeling bias and gradient imbalance caused by excessive differences in the numerical ranges of data from different dimensions. 3σ principle detection identifies outlier data points, replacing outliers that deviate from the normal data distribution with the mean of neighboring data to remove noise interference. After the above preprocessing, the final result is... .

[0014] 2. Regarding step S2: It includes four sub-steps: basic feature mapping, hierarchical dimensional pruning, adaptive initial weight calculation, and multi-scale feature fusion.

[0015] In (2.1), the basic feature mapping will Mapping to a high-dimensional feature space yields the basic features. This amplifies subtle differences in the original data, enhances feature representation capabilities, and provides a sufficient dimensional framework for subsequent multi-scale pruning, thus preventing multi-scale stratification failure due to insufficient basic feature dimensions.

[0016] (2.2) Hierarchical dimensional pruning prunes the basic features into K nested features of different scales. K can be adaptively adjusted according to data complexity. For complex dynamic scenarios, 3-4 scales are preferred. Each scale corresponds to feature information of different granularities. Coarse-scale features focus on the global structure, while fine-scale features focus on local details. Nested feature decomposition is achieved by decreasing the dimensions, ensuring that small-scale features are effective subsets of large-scale features. This preserves the hierarchical correlation of features and achieves a balance between the global and the detailed, avoiding the fragmentation of features across multiple scales.

[0017] (2.3) Adaptive initial weight calculation: In order to quantify the information contribution of features at each scale, avoid the subjective bias of manually setting weights, and ensure that the weight allocation fits the actual information content of the features, this invention uses the information entropy function to calculate the initial weight (information entropy weight) of features at each scale. This method can objectively allocate weights based on the information content of the features themselves. The larger the information content of the scale feature and the higher the contribution to reconstruction, the higher the weight is assigned. No manual intervention is required. It adapts to the feature distribution of different datasets and realizes adaptive weight optimization.

[0018] (2.4) Multi-scale feature fusion: The nested features at each scale are weighted and fused according to the initial weights (information entropy weights) to integrate the core information of the whole scale and obtain the multi-scale fused feature F at a single time step. t This method efficiently integrates features of different granularities, taking into account both global structure and local details. It achieves complementary advantages of multi-scale features, eliminates redundant feature interference, and retains core information while compressing feature dimensions. This provides high-quality input for subsequent dynamic Gaussian modeling and avoids overfitting caused by cluttered features.

[0019] 3. Regarding step S3, because traditional Gaussian kernel functions use fixed static parameters, they cannot adapt to the temporal distribution drift of dynamic data, resulting in a significant decrease in modeling accuracy over time. This step aims to break the limitations of static parameters, introduce time dependence, and construct a dynamic kernel function that updates dynamically over time.

[0020] (3.1) A dynamic kernel function is adopted, and the kernel parameters can be updated iteratively with each time step, which fits the feature distribution of each frame of data in real time, accurately captures the temporal changes of dynamic data, and overcomes the defects of static model fitting lag and poor adaptability. The expression is k t (F i ,F j ).

[0021] (3.2) In the dynamic kernel function, The signal strength at the current time step is used to characterize the feature signal strength and dynamically reflect the discreteness of the feature data; l(t) is used to control the feature similarity fitting range and adjust the model’s sensitivity to feature differences. It is used to measure the difference between any two features and accurately characterize feature similarity.

[0022] (3.3) constructed The update formula for l(t) is here. The update of l(t) relies entirely on the statistical characteristics of the data itself, requiring no manual intervention. It can track changes in data distribution while ensuring the stability of parameter updates, avoiding modeling failure due to drastic parameter fluctuations. When t=1, the initial value of the signal variance is used. The initial value of the length scale parameter l(0) is preset in this invention. =0.5, l(0)=1, sliding window length τ=5, improve parameter stability through local window statistics, Med(⋅) is the median function, which can effectively reduce the interference of outliers on parameter updates, avoid parameter offset caused by individual outliers, and improve the stability and reliability of parameter updates.

[0023] 4. Regarding step S4, dynamic Gaussian process modeling. This step first constructs the temporal covariance matrix, then performs probabilistic modeling on the multi-scale fused feature sequences, defines the prior distribution of the Gaussian process, and then... k , l(0) is used as a learnable parameter for training and updating.

[0024] (4.1) Constructing the temporal covariance matrix This invention employs probabilistic modeling of multi-scale fused feature sequences and defines a Gaussian process prior distribution. The aim is to transform the feature sequences into a probabilistic model, leveraging the nonlinear fitting capability of the Gaussian process to achieve accurate modeling and fitting of dynamic data while preserving the model's probabilistic interpretability, facilitating subsequent evaluation of reconstruction reliability. In this invention, m(F) is the mean function, and a zero-mean value is used to simplify calculations, reduce model complexity, and minimize noise variance. Used to counteract data noise interference.

[0025] (4.2) During training, the loss function is first selected as the MSE error L. MSE Then, define the objective function and the iteration stopping condition. The parameter optimization objective is... argmin is the argmin function, used to return the parameter value that minimizes the objective function. The iteration stops when the following two conditions are met: condition 1 and / or condition 2: Condition 1: Condition 2: iter ≥ N;

[0026] Where iter is the current iteration number, and Loss is... iter Loss is the loss function value for the current iteration number. iter-100 The loss function value is the value when the number of iterations is (iter-100). The convergence threshold preset for the loss function. The threshold for the change in the loss function is denoted by N, which is the maximum number of iterations, typically N=500. After the parameter iterations converge, the model has the ability to adapt to dynamic 3D data distributions and can be used for 3D reconstruction at subsequent time steps to be predicted.

[0027] 5. Regarding step S5: posterior mean The final 3D reconstruction output value, which is the optimal estimate of the 3D reconstruction at the time step to be predicted, is the posterior variance. The smaller the variance, the more reliable the reconstruction result.

[0028] Compared with the prior art, the advantages of the present invention are as follows: (1) More comprehensive multi-scale feature representation: In step S2, the present invention achieves full-scale feature capture through four sub-steps: basic feature mapping, hierarchical feature clipping, adaptive weight calculation based on information entropy, and multi-scale feature fusion. This preserves core features at different scales, eliminates redundant information, provides a high-quality feature base for 3D reconstruction, and greatly improves the accuracy of detail reconstruction.

[0029] (2) More adaptable dynamic modeling: Design a time-dependent dynamic Gaussian kernel function, update kernel parameters in real time based on time-series characteristic statistics, accurately track dynamic three-dimensional data distribution changes, and overcome the problems of lag and poor drift adaptation of static Gaussian model fitting.

[0030] (3) Closed-loop optimization is more robust: a prediction error feedback mechanism is constructed to realize the joint iterative optimization of nested representation feature weights and dynamic Gaussian parameters. The model can learn the distribution changes of dynamic data autonomously and adjust the parameters adaptively. Even in the face of complex and ever-changing dynamic scenarios, it can still ensure the long-term accuracy and robustness of 3D reconstruction and realize the continuous and stable reconstruction of dynamic 3D data.

[0031] (4) The method is more versatile: it is applicable to various dynamic high-dimensional 3D data reconstruction scenarios, without the need to customize parameters for specific datasets, and balances reconstruction accuracy and computational efficiency, with a low threshold for engineering implementation.

[0032] In summary, this invention combines comprehensive multi-scale features, adaptive dynamic modeling, and robust closed-loop optimization, which can significantly improve the reconstruction accuracy and detail reproduction of dynamic 3D data. It is applicable to various scenarios such as dynamic point clouds and dynamic meshes, and has strong engineering practical value. Attached Figure Description

[0033] Figure 1 This is a flowchart of the present invention; Figure 2 A flowchart for generating multi-scale fusion features; Figure 3 This is a flowchart of parameter updates during a training process. Detailed Implementation

[0034] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0035] Example 1: See Figures 1 to 3 A nested representation 3D reconstruction method based on a dynamic Gaussian framework includes the following steps: S1, acquire the dynamic 3D data sequence X of the dynamic 3D scene and preprocess the dynamic 3D data sequence. In the formula, The original three-dimensional data x at time step t t The corresponding preprocessed data, where T is the total number of time steps; S2, construct the time-series feature sequence F. The multi-scale fusion feature F at time step t t The construction method includes steps S21 to S22; S21, will Mapping to a high-dimensional feature space yields the basic features. Then, the layers are further pruned into K nested features of different scales. The nested features at scale k are... The initial weights ω of features at each scale are calculated using the information entropy function. k , 1≤k≤K; S22, sort the K nested features by ωk Weighted fusion of multi-scale fusion features F at time step t t ; S3 defines the dynamic kernel function for time step t; , , In the formula, F i F j These are the multi-scale fusion features at time steps i and j, respectively. Let be the dynamic kernel function of the multi-scale fusion features at time step t over two time steps. Let l(t) be the signal variance at time step t, and l(t) be the length scale parameter of time step t. For Euclidean distance, Var(F) 1:t ) is F1~F t The sample variance The length of the sliding window. Let F represent the feature sequence obtained with two time steps as the two endpoints, where Med(⋅) is the median function, and the initial value of the signal variance is preset. =0.5, the initial value of the length scale parameter is l(0)=1; S4, Dynamic Gaussian process modeling and parameter optimization, including S41~S43; S41, Construct the time series covariance matrix K t K t element in row i and column j , For noise variance, The Kronecker function; S42, Define the output sequence of a Gaussian process. Prior distribution of Gaussian process GP(⋅,⋅) is a Gaussian process, m(F)=0 is the mean function, and y t The predicted three-dimensional data for time t; S43, ω k , Using l(0) as learnable parameters, gradient descent is used to minimize y and The MSE error is updated until the preset iteration stop condition is met; S5, Given a temporal feature sequence F, multi-scale fusion features for the time step to be predicted. Based on Bayesian inference, the posterior prediction distribution of the Gaussian process is derived, and the posterior mean is calculated. and posterior variance ,Will As the optimal estimate for the 3D reconstruction of the time step to be predicted.

[0036] Example 2: See Figures 1-3 Based on Example 1, in this example, S1 specifically involves: acquiring the raw 3D data of the dynamic 3D scene at continuous time steps, using the raw 3D data x at time step t. t Constructing dynamic three-dimensional data sequences ; For x t The Z-score standardization method is used to eliminate data dimensions, and then the 3σ principle is used to detect and remove outliers to obtain preprocessed data at time step t. This constitutes a preprocessed dynamic three-dimensional data sequence. ; S21 includes Sa1~Sa3; Sa1, according to the formula Obtain basic features Where W0 and b0 are the weight matrix and bias during mapping, respectively. , , D and d0 respectively and The feature dimension, d0 > D; Sa2, with K preset feature dimensions, where the k-th feature dimension d k =α k d0, α∈(0,1) is the scale decay coefficient, in Before the cut Nested features of dimension k constituting scale k are ; Sa3, ω is calculated according to the following formula k : , In the formula, H(⋅) is the information entropy function, p kj This is the probability density of dimension j at scale k, calculated based on feature component normalization.

[0037] S22 specifically refers to: [details of each] Based on the trailing zero-padding method, map it to the basic feature dimension to obtain the corresponding padded features. Then, F is obtained by weighted fusion according to the formula. t , .

[0038] In S43, the MSE error L MSE Calculate according to the following formula: .

[0039] In S5, the Gaussian process posterior prediction distribution satisfy: , In the formula, , , , These represent the predicted 3D data for the time step to be predicted, multi-scale fusion features, posterior mean, and posterior variance, respectively. It follows a Gaussian distribution, and , Calculate according to the following formula: , .

[0040] Example 3: See Figures 1 to 3 Based on Example 1, the following experiments were conducted to illustrate the effects of the present invention: Experimental Design: Datasets: Public datasets such as Deforming Things 4D and D-FAUST are used. This embodiment selects the Deforming Things 4D dataset.

[0041] Experimental environment: Hardware is NVIDIA RTX 3090 GPU, software environment is PyTorch 2.1.

[0042] Experimental groups: including experimental group and control group 1 and control group 2.

[0043] Experimental Group: This invention presents a nested representation 3D reconstruction method based on a dynamic Gaussian framework, used to process dynamic 3D data with temporal variations. This method first maps the original data to a multi-scale feature space using nested representation techniques, and then adaptively calculates the initial weights for each scale using information entropy. Subsequently, a dynamic Gaussian kernel function that is recursively updated over time step t is constructed. This enables real-time capture of non-stationary data distributions; finally, high-precision reconstruction results are output through Bayesian posterior inference, and the initial parameters are optimized using closed-loop feedback of prediction errors.

[0044] Control group 1: Traditional single-scale Gaussian process 3D reconstruction method.

[0045] Control group 2: Multi-scale nested representation reconstruction method, in addition to steps S1~S5 of this invention, does not use the dynamic kernel function of time step t of this invention in step S3. Do not use time-varying Instead of l(t), a set of fixed, time-invariant kernel parameters is used: signal variance σ 2 The radial basis function kernel is constructed using a length scale l, and no σ is performed in step S4. 2 The update of l is performed using only gradient descent to update ω. kThe iteration continues until a preset stopping condition is met. The rest is the same as in this invention.

[0046] Metrics Selection: The performance metrics selected include reconstruction accuracy, Chamfer distance, and single-frame inference time. Among them, Chamfer distance is the chamfer distance, a classic metric for evaluating the similarity between two point clouds. It quantifies shape differences by calculating the nearest neighbor distance from each point in one point set to another point set.

[0047] Experimental results: The performance indicators of the present invention and the control group are shown in Table 1 below: Table 1: Comparison of Performance Indicators of Different Methods Method Name Reconstruction accuracy (%) Chamfer distance (mm) Single-frame inference time (ms) This invention 92.7 5.42 42 Control group 1 78.5 12.85 115 Control group 2 84.2 8.16 58 Data analysis: The method of this invention significantly outperforms the two control groups in reconstruction accuracy, with a smaller Chamfer distance, indicating more accurate 3D structure reconstruction and more complete detail preservation; single-frame inference time is shorter, and real-time performance is stronger. Thanks to nested representation multi-scale feature capture and dynamic Gaussian kernel temporal adaptive optimization, this method can better adapt to dynamic data distribution changes, and has obvious advantages in reconstruction robustness and accuracy in motion deformation scenarios.

[0048] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A nested representation 3D reconstruction method based on a dynamic Gaussian frame, characterized in that, Includes the following steps: S1, acquire the dynamic 3D data sequence X of the dynamic 3D scene and preprocess the dynamic 3D data sequence. In the formula, The original three-dimensional data x at time step t t The corresponding preprocessed data, where T is the total number of time steps; S2, construct the time-series feature sequence F. The multi-scale fusion feature F at time step t t The construction method includes steps S21 to S22; S21, will Mapping to a high-dimensional feature space yields the basic features. Then, the layers are further pruned into K nested features of different scales. The nested features at scale k are... The initial weights ω of features at each scale are calculated using the information entropy function. k , 1≤k≤K; S22, sort the K nested features by ω k Weighted fusion of multi-scale fusion features F at time step t t ; S3 defines the dynamic kernel function for time step t; ， ， In the formula, F i F j These are the multi-scale fusion features at time steps i and j, respectively. Let be the dynamic kernel function of the multi-scale fusion features at time step t over two time steps. Let l(t) be the signal variance at time step t, and l(t) be the length scale parameter of time step t. For Euclidean distance, Var(F) 1:t ) is F1~F t The sample variance The length of the sliding window. Let F represent the feature sequence obtained with two time steps as the two endpoints, where Med(⋅) is the median function, and the initial value of the signal variance is preset. =0.5, the initial value of the length scale parameter is l(0)=1; S4, Dynamic Gaussian process modeling and parameter optimization, including S41~S43; S41, Construct the time series covariance matrix K t K t element in row i and column j , For noise variance, The Kronecker function; S42, Define the output sequence of a Gaussian process. Prior distribution of Gaussian process GP(⋅,⋅) is a Gaussian process, m(F)=0 is the mean function, and y t The predicted three-dimensional data for time t; S43, ω k , Using l(0) as learnable parameters, gradient descent is used to minimize y and The MSE error is updated until the preset iteration stop condition is met; S5, Given a temporal feature sequence F, multi-scale fusion features for the time step to be predicted. Based on Bayesian inference, the posterior prediction distribution of the Gaussian process is derived, and the posterior mean is calculated. and posterior variance ,Will As the optimal estimate for the 3D reconstruction of the time step to be predicted.

2. The nested representation 3D reconstruction method based on a dynamic Gaussian frame according to claim 1, characterized in that, S1 specifically refers to: Obtain the raw 3D data of a dynamic 3D scene at continuous time steps, using the raw 3D data x at time step t. t Constructing dynamic three-dimensional data sequences ; For x t The Z-score standardization method is used to eliminate data dimensions, and then the 3σ principle is used to detect and remove outliers to obtain preprocessed data at time step t. This constitutes a preprocessed dynamic three-dimensional data sequence. .

3. The nested representation 3D reconstruction method based on a dynamic Gaussian frame according to claim 1, characterized in that, S21 includes Sa1~Sa3; Sa1, the basic features are obtained by mapping according to the following formula. , ， In the formula, W0 and b0 are the weight matrix and bias during mapping, respectively. , , D and d0 respectively and The feature dimension, d0 > D; Sa2, with K preset feature dimensions, where the k-th feature dimension d k =α k d0, α∈(0,1) is the scale decay coefficient, in Before the cut Nested features of dimension k constituting scale k are ; Sa3, ω is calculated according to the following formula k : ， In the formula, H(⋅) is the information entropy function, p kj This is the probability density of dimension j at scale k, calculated based on feature component normalization.

4. The nested representation 3D reconstruction method based on a dynamic Gaussian frame according to claim 1, characterized in that, S22 specifically refers to: [details of each] Based on the trailing zero-padding method, map it to the basic feature dimension to obtain the corresponding padded features. Then, F is obtained by weighted fusion according to the formula. t , .

5. The nested representation 3D reconstruction method based on a dynamic Gaussian frame according to claim 1, characterized in that, In S43, the MSE error L MSE Calculate according to the following formula: 。 6. The nested representation 3D reconstruction method based on a dynamic Gaussian frame according to claim 1, characterized in that, In S5, the Gaussian process posterior prediction distribution satisfy: ， In the formula, , , , These represent the predicted 3D data for the time step to be predicted, multi-scale fusion features, posterior mean, and posterior variance, respectively. It follows a Gaussian distribution, and , Calculate according to the following formula: ， 。

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