Fetal brain magnetic resonance three-dimensional reconstruction method based on density gated geometric prior

Abstract

The application discloses a fetal brain magnetic resonance three-dimensional reconstruction method based on a density gated geometric prior, performs pretreatment on a fetal brain magnetic resonance two-dimensional slice stack to obtain an input observation slice dataset; based on the input observation slice dataset, slice space transformation and estimated volume are updated to obtain final space transformation and a rough estimated volume of each slice; based on the input observation slice dataset and the final space transformation of the slice, a physical density map is constructed, and based on the rough estimated volume and the physical density map, a geometric prior volume is generated; based on the geometric prior volume, a three-dimensional Gaussian primitive is initialized to obtain an initial three-dimensional Gaussian field, and based on the geometric prior volume and the initial three-dimensional Gaussian field, a pre-fitted three-dimensional Gaussian field is obtained; based on the input observation slice dataset, the final space transformation and the pre-fitted three-dimensional Gaussian field, a consistency loss is constructed; based on the geometric prior volume, the pre-fitted three-dimensional Gaussian field and the consistency loss, a final three-dimensional Gaussian field is obtained, and a fetal brain magnetic resonance three-dimensional reconstruction volume is output.

Description

Technical Field

[0001] This invention relates to the field of medical image reconstruction technology, and more specifically, to a method for rapid three-dimensional Gaussian reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors. Background Technology

[0002] Fetal brain magnetic resonance imaging (MRI) provides important information for prenatal diagnosis and assessment of fetal brain development. However, due to unpredictable movements that may occur in the fetus and mother during the scanning process, clinically acquired fetal brain MRI images are usually two-dimensional thick slice images with multiple sets of motion misalignments, making it difficult to directly obtain structurally continuous three-dimensional high-resolution volumetric images.

[0003] Existing slice-to-volume reconstruction methods typically require registration of 2D slices, point spread function modeling, and super-resolution reconstruction. Traditional iterative methods are computationally time-consuming, while implicit neural representation methods often require extensive sampling during simulated slice imaging, making it difficult to balance reconstruction quality and speed.

[0004] While 3D Gaussian primitives can quickly reconstruct 3D volumes analytically, in situations where fetal movement is significant, slice intervals are large, slice quality is poor, or effective observation is insufficient, independently optimized Gaussian primitives lack global geometric constraints and are prone to problems such as structural distortion, artifacts, and discontinuities in anatomical structures. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects and shortcomings of the prior art and provide a method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors. Based on two-dimensional fetal brain magnetic resonance slices of input observation, a physical density map reflecting the sufficiency of acquisition and observation is constructed. A prior volume of structural continuity is generated using density-gated geometric priors, and the prior volume is used for the initialization and optimization constraints of three-dimensional Gaussian primitives. This improves the structural stability of the reconstruction results under low-quality input conditions while maintaining the advantages of fast three-dimensional Gaussian reconstruction.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for three-dimensional reconstruction of the fetal brain using magnetic resonance imaging based on density-gated geometric priors includes the following steps:

[0008] Obtain the stack of two-dimensional slices from fetal brain magnetic resonance imaging (MRI), preprocess the stack of two-dimensional slices from fetal brain MRI, and obtain the input observation slice dataset;

[0009] Based on the input observation slice dataset, the slice spatial transformation and estimated volume are updated alternately to obtain the final spatial transformation and coarse volume of each slice;

[0010] Based on the input observation slice dataset and the final spatial transformation of the slice, a physical density map is constructed. Based on the coarse volume estimate and the physical density map, a geometric prior volume is generated through density-gated residual repair.

[0011] The three-dimensional Gaussian primitives are initialized based on the geometric prior volume to obtain the initial three-dimensional Gaussian field. Based on the geometric prior volume and the initial three-dimensional Gaussian field, the prior volume is fitted to obtain the prefitted three-dimensional Gaussian field.

[0012] Based on the input observation slice dataset, the final spatial transformation, and the prefitted 3D Gaussian field, the slice imaging process is simulated to obtain the predicted slice. Based on the intensity difference between the predicted slice and the input observation slice, a data consistency loss is constructed.

[0013] Based on the geometric prior volume, the prefitted 3D Gaussian field, and the data consistency loss, the 3D Gaussian primitives are updated to obtain the final 3D Gaussian field. Based on the final 3D Gaussian field, the 3D reconstructed volume of the fetal brain magnetic resonance imaging is output.

[0014] Furthermore, a stack of two-dimensional fetal brain magnetic resonance imaging (MRI) slices is obtained, and the stack of fetal brain MRI slices is preprocessed to obtain the input observation slice dataset, specifically:

[0015] The fetal brain magnetic resonance imaging (MRI) two-dimensional slice stack and its acquisition parameters are obtained. The two-dimensional slice stack is then processed by image reading, brain region mask acquisition, invalid background removal, intensity truncation and intensity normalization. Based on the initial affine matrix of each slice, the homogeneous pixel coordinates of the effective pixels are converted into initial world coordinates to obtain the input observation slice dataset.

[0016] The input observation slice dataset includes the intensity of the input observation slice image after intensity preprocessing but without spatial resampling, homogeneous pixel coordinates, initial slice spatial coordinates, initial slice affine matrix, slice thickness, pixel spacing, and slice center coordinates, which serve as the unified input for subsequent slice registration, physical density calculation, and 3D Gaussian query.

[0017] Furthermore, based on the input observation slice dataset, the slice spatial transformation and estimated volume are alternately updated to obtain the final spatial transformation and coarse volume estimate for each slice, specifically as follows:

[0018] Initialize the nine-dimensional spatial transformation representation of each slice, and do not use the volume estimated in the previous round in the first iteration;

[0019] In the In the round of iteration, the first step is based on the input observation slice. Subsequent rounds are based on the input observation slice, the spatial transformation of the previous round, and the simulated slice generated by the estimated volume of the previous round. The nine-dimensional spatial transformation residual parameters of each slice are predicted through the slice-to-volume registration network. The residual parameters are added element by element to the nine-dimensional spatial transformation representation of the previous round, and the updated nine-dimensional spatial transformation representation is converted into the rigid spatial transformation of the current round.

[0020] The second step involves performing point spread function back projection and super-resolution reconstruction on the input observation slices based on the updated spatial transformation to obtain the estimated volume for this round. The updated spatial transformation and estimated volume are then passed to the next iteration to progressively improve the accuracy of slice registration and volume estimation. The spatial transformation obtained in the final iteration serves as the final spatial transformation of each slice relative to the 3D reconstructed world coordinate system. The estimated volume obtained in the final round before density-gated residual repair is used as the final round coarse volume estimate. .

[0021] Furthermore, based on the input observation slice dataset and the final spatial transformation of the slices, a physical density map is constructed, specifically as follows:

[0022] The point spread function during the slicing acquisition process is modeled as a Gaussian point spread function, and then subjected to the final spatial transformation. The point spread function contributions of all input observation slices are accumulated to obtain the physical density map. Its calculation formula is expressed as:

[0023] ;

[0024] in, This indicates the position in the 3D reconstructed world coordinate system. This indicates the total number of observed slices. Indicates the first The pixel field of each slice Represents the pixel coordinates of the slice. Indicates the first The final pose of each slice determines the local physical position of the slice corresponding to the pixel coordinates and maps it to the position in the 3D reconstructed world coordinate system. Indicates according to the first The point spread function is determined by the in-plane pixel spacing, slice thickness and spatial orientation of each slice;

[0025] The initial slice affine matrix is ​​used to establish the initial coordinate mapping. The final spatial transformation serves as the current absolute coordinate mapping used in subsequent steps and is not superimposed on the initial slice affine matrix. The physical density map is used to represent the degree to which each location in the 3D reconstructed world coordinate system is covered by the input observation slice.

[0026] Furthermore, based on the coarsely estimated volume and physical density map, a geometric prior volume is generated through density-gated residual repair, specifically:

[0027] First, convert the physical density map into observation confidence scores. Then, the coarse volume and physical density map are combined by channel and input into the pre-trained residual repair network. ; Calculate the gating function based on the observation confidence level The residual repair strength is adjusted using a gating function, and the gated residual is added to the coarsely estimated volume to obtain the geometric prior volume. ;

[0028] The formulas for calculating the observation confidence level, the gating function, and the geometric prior volume are expressed as follows:

[0029] ;

[0030] ;

[0031] ;

[0032] in, This indicates a complete rough estimate of the volume. Represents the complete physical density map. This represents an exponential function with the natural constant e as its base. and Indicates the preset gating coefficient, and .

[0033] Furthermore, based on the geometric prior volume initialization of the three-dimensional Gaussian primitives, the initial three-dimensional Gaussian field is obtained, specifically as follows:

[0034] Effective voxels are selected in the foreground region of the geometric prior volume according to the intensity threshold. The coordinates of the effective voxels are transformed to the 3D reconstructed world coordinate system, and the center position of each 3D Gaussian primitive is obtained by sampling based on the transformed coordinates. The intensity parameters of each 3D Gaussian primitive are initialized based on the corresponding voxel intensity. Simultaneously initialize the scaling parameters of each 3D Gaussian primitive. and the rotation parameters used to generate the rotation matrix, and convert the rotation parameters into the rotation matrix. And construct a scale matrix based on the scale parameters; thus obtaining the set of three-dimensional Gaussian primitives. Represented as:

[0035] ;

[0036] ;

[0037] ;

[0038] in, Indicates the number of three-dimensional Gaussian primitives. Indicates the first The covariance matrix of a three-dimensional Gaussian primitive. This represents the 3×3 rotation matrix obtained by transforming the rotation parameters of the j-th 3D Gaussian primitive. Let represent the diagonal scaling matrix of the j-th 3D Gaussian primitive, and diag(·) denotes the operation of constructing a diagonal matrix from the listed elements. , and These represent the scale components of the j-th three-dimensional Gaussian primitive along the three coordinate axes, respectively.

[0039] Furthermore, based on the geometric prior volume and the initial three-dimensional Gaussian field, a prior volume fitting is performed to obtain the prefitted three-dimensional Gaussian field, specifically as follows:

[0040] Three-dimensional points are sampled in the foreground region of the geometric prior volume, and the initial three-dimensional Gaussian field is directly queried in the three-dimensional reconstructed world coordinate system to obtain the Gaussian predicted intensity. And predict the intensity using Gaussian. With geometric prior volume The difference between them constructs the volume fitting loss. The volume fitting loss is expressed as:

[0041] ;

[0042] ;

[0043] in, The foreground region representing the geometric prior volume. Indicates the first A scale vector of a three-dimensional Gaussian primitive. This represents the preset target scale vector. This is used to constrain the scale of each 3D Gaussian primitive to be close to the target scale. Indicates the scale regularization weight. This represents the L2 norm.

[0044] Furthermore, based on the input observation slice dataset, the final spatial transformation, and the pre-fitted 3D Gaussian field, the slice imaging process is simulated to obtain predicted slices. A data consistency loss is constructed based on the intensity difference between the predicted slices and the input observation slices, specifically:

[0045] by As the first The initial values ​​of each slice pose are introduced, and the residual rigidity transformation to be optimized is introduced. The residual rigid transformation is defined in the 3D reconstructed world coordinate system and rotated around the center of the corresponding slice. It is applied to the 3D query position obtained from the final spatial transformation to obtain the current corrected spatial transformation. ;

[0046] For the Pixel coordinates in a slice ,pass Obtain its 3D query position in the 3D reconstructed world coordinate system; according to the first The thickness of each slice and the in-plane pixel spacing generate the point spread function covariance in the slice coordinate system. and will the Covariance of a three-dimensional Gaussian primitive With the rotation matrix of the current slice The equivalent covariance under slice observations is obtained by analytically superimposing the covariances of the transformed point spread function. :

[0047] ;

[0048] ;

[0049] In the formula, the symbol " " indicates the composition of rigid spatial transformations, with the composition order being to apply the final spatial transformation first, followed by the residual rigid transformation;

[0050] Based on equivalent covariance, three-dimensional Gaussian primitives within the neighborhood of the three-dimensional query location are selected from the prefitted three-dimensional Gaussian field, and the calculation of each three-dimensional Gaussian primitive at the 1st... slice pixel coordinates Analysis weight at the location The analytical weights are then normalized to obtain the predicted intensity. Arrange all predicted intensities within the slice pixel domain according to their original pixel positions to obtain the first... 1. Predict a slice; construct a data consistency loss based on the intensity difference between the predicted slice and the input observed slice. :

[0051] ;

[0052] ;

[0053] ;

[0054] in, express The rotating part, Indicates distance from the 3D query location Recent A set of three-dimensional Gaussian primitives, This represents the number of nearest-neighbor 3D Gaussian primitives. This represents a preset positive number used to ensure numerical stability. Indicates the first Intensity scaling factor for each slice, This represents the k-th predicted slice. Indicates the first One input observation slice, This represents the L1 norm calculated over the slice pixel domain.

[0055] Furthermore, based on the geometric prior volume, the prefitted 3D Gaussian field, and the data consistency loss, the 3D Gaussian primitives are updated to obtain the final 3D Gaussian field. Based on the final 3D Gaussian field, the 3D reconstructed volume of the fetal brain magnetic resonance imaging is output, specifically:

[0056] Sample 3D points in the reconstructed 3D world coordinate system and calculate the predicted volume of the current 3D Gaussian field. With geometric prior volume Prior distillation loss between Furthermore, the a priori distillation loss, data consistency loss, and scaling regularization term are combined to obtain the joint loss. :

[0057] ;

[0058] ;

[0059] in, Indicates the first Prior distillation weights in the next iteration; according to the preset iteration interval, make The initial weights are linearly decayed to the final weights, so that the early optimization focuses on maintaining the global structure provided by the geometric prior, and the later optimization focuses on fitting the input observation slices.

[0060] Based on joint loss The center position, intensity, scale, and rotation parameters of the three-dimensional Gaussian primitive, as well as the residual motion parameters of each slice, are updated together to obtain the final three-dimensional Gaussian field. Then, the intensity of the final three-dimensional Gaussian field is calculated on the target three-dimensional mesh to obtain the high-resolution three-dimensional fetal brain magnetic resonance reconstruction volume.

[0061] Furthermore, the 3D Gaussian primitive is determined by the center position, intensity, scale, and rotation parameters; the prior volume fitting and simulated slice imaging process does not use the method of rasterizing the 3D Gaussian primitive after projecting it onto the 2D imaging plane, but directly calculates the contribution of the 3D Gaussian primitive to the 3D query position in the 3D reconstructed world coordinate system.

[0062] For the 3D query location, a preset number of 3D Gaussian primitives closest to the 3D query location are selected through nearest neighbor retrieval. Spatial weights are calculated for each primitive and then normalized and weighted to obtain the intensity of the 3D Gaussian field at the 3D query location.

[0063] ;

[0064] ;

[0065] in, This represents the unnormalized spatial weight of the j-th 3D Gaussian primitive at the 3D query position x. Represents the closest to x A set of three-dimensional Gaussian primitives; the three-dimensional query location includes three-dimensional sampling points in the geometric prior volume, target three-dimensional mesh points, or slice pixel locations mapped to the three-dimensional reconstructed world coordinate system by the current corrected spatial transformation.

[0066] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0067] This invention describes the sufficiency of observation at each location in the three-dimensional reconstructed world coordinate system using a physical density map, thus linking the generation process of geometric priors with the physical process of fetal brain magnetic resonance imaging slice acquisition, and enabling the differentiation between areas with sufficient observation and areas with insufficient observation.

[0068] This invention initializes three-dimensional Gaussian primitives with density-gated geometric prior volume, enabling the Gaussian primitives to have a more stable overall anatomical structure at the start of optimization, thereby reducing the possibility of structural distortion or local collapse of the Gaussian primitives under low-quality input conditions.

[0069] This invention employs a two-stage optimization approach: prior volume fitting and input observation slice fitting. First, a stable three-dimensional structure is established based on the geometric prior volume, and then image details are restored based on the input observation slices, thereby balancing the stability of the reconstructed structure and the ability to restore local details.

[0070] This invention utilizes the analytical covariance superposition relationship between three-dimensional Gaussian primitives and Gaussian point spread functions, and directly queries neighboring three-dimensional Gaussian primitives in the three-dimensional reconstruction world coordinate system, reducing the amount of random sampling, two-dimensional projection and rasterization calculations, which helps to maintain the reconstruction speed.

[0071] This invention introduces prior distillation constraints in the input observation slice fitting stage, so that the three-dimensional Gaussian field is subject to geometric prior constraints while fitting the intensity of the input observation slice, thereby improving the robustness of the reconstruction results in cases such as significant fetal movement, poor slice quality, or insufficient effective observation. Attached Figure Description

[0072] Figure 1This is a schematic diagram of a three-dimensional reconstruction method for fetal brain magnetic resonance imaging based on density-gated geometric priors.

[0073] Figure 2 This is a flowchart of a method for three-dimensional reconstruction of the fetal brain using magnetic resonance imaging based on density-gated geometric priors.

[0074] Figure 3 This is a schematic diagram illustrating the principle of the alternating iterative process of slice transformation update and volume estimation.

[0075] Figure 4 This is a schematic diagram of the density-gated geometric prior generation process.

[0076] Figure 5 This is a schematic diagram of the residual repair network. Detailed Implementation

[0077] The following description, in conjunction with the accompanying drawings and specific embodiments, further illustrates the present invention's method for three-dimensional reconstruction of the fetal brain based on density-gated geometric priors using magnetic resonance imaging.

[0078] Please see Figure 1 This invention discloses a method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors, comprising the following steps:

[0079] S1: Obtain the stack of two-dimensional fetal brain magnetic resonance imaging (MRI) slices, preprocess the stack of two-dimensional fetal brain MRI slices, and obtain the input observation slice dataset.

[0080] S2: Based on the input observation slice dataset, alternately update the slice spatial transformation and estimated volume to obtain the final spatial transformation and coarse volume estimate of each slice;

[0081] S3: Based on the input observation slice dataset and the final spatial transformation of the slice, construct a physical density map. Based on the coarse volume estimate and the physical density map, generate a geometric prior volume through density-gated residual repair.

[0082] S4: Initialize the three-dimensional Gaussian primitives based on the geometric prior volume to obtain the initial three-dimensional Gaussian field. Based on the geometric prior volume and the initial three-dimensional Gaussian field, perform prior volume fitting to obtain the prefitted three-dimensional Gaussian field.

[0083] S5: Based on the input observation slice dataset, final spatial transformation and prefitted 3D Gaussian field, simulate the slice imaging process to obtain the predicted slice. Construct a data consistency loss based on the intensity difference between the predicted slice and the input observation slice.

[0084] S6: Based on the geometric prior volume, the prefitted 3D Gaussian field and the data consistency loss, update the 3D Gaussian primitives to obtain the final 3D Gaussian field. Based on the final 3D Gaussian field, output the 3D reconstructed volume of the fetal brain magnetic resonance imaging.

[0085] Step S1: Obtain the fetal brain magnetic resonance two-dimensional slice stack and its acquisition parameters. Perform image reading, brain region mask acquisition, invalid background removal, intensity truncation and intensity normalization on the two-dimensional slice stack. Based on the initial affine matrix of each slice, convert the homogeneous pixel coordinates of the effective pixels into the initial world coordinates to obtain the input observation slice dataset.

[0086] The input observation slice dataset includes the intensity of the input observation slice image after intensity preprocessing but without spatial resampling, homogeneous pixel coordinates, initial slice spatial coordinates, initial slice affine matrix, slice thickness, pixel spacing, and slice center coordinates, which serve as the unified input for subsequent slice registration, physical density calculation, and 3D Gaussian query.

[0087] Step S2: Based on the input observation slice dataset, perform a preset number of rounds of alternating slice transformation updates and volume estimation in one network forward inference to obtain the final spatial transformation of each slice relative to the 3D reconstructed world coordinate system. and the final rough volume estimate .

[0088] Specifically, the nine-dimensional spatial transformation representation of each slice is initialized, and the volume estimated in the previous round is not used in the first iteration;

[0089] In the In the round of iteration, the first step is based on the input observation slice. Subsequent rounds are based on the input observation slice, the spatial transformation of the previous round, and the simulated slice generated by the estimated volume of the previous round. The nine-dimensional spatial transformation residual parameters of each slice are predicted through the slice-to-volume registration network. The residual parameters are added element by element to the nine-dimensional spatial transformation representation of the previous round, and the updated nine-dimensional spatial transformation representation is converted into the rigid spatial transformation of the current round.

[0090] The second step involves performing point spread function back projection and super-resolution reconstruction on the input observation slices based on the updated spatial transform, yielding the estimated volume for this round. The updated spatial transform and estimated volume are then passed to the next iteration to progressively improve the accuracy of slice registration and volume estimation. The spatial transform obtained in the final iteration serves as the basis for further analysis. The estimated volume obtained in the final round before density-gated residual repair is used as... .

[0091] Step S3, based on slice thickness, pixel spacing, slice spatial coordinates, and the spatial transformation obtained in the last round. A physical density map is constructed. The physical density map is used to represent the degree to which each location in the 3D reconstructed world coordinate system is covered by the input observation slice.

[0092] Specifically, the point spread function during the slicing acquisition process is modeled as a Gaussian point spread function, according to the final spatial transformation. The point spread function contributions of all input observation slices are accumulated to obtain the physical density map. Its calculation formula is expressed as:

[0093] ;

[0094] in, This indicates the position in the 3D reconstructed world coordinate system. This indicates the total number of observed slices. Indicates the first The pixel field of each slice Represents the pixel coordinates of the slice. Indicates the first The final pose determination of each slice maps the local physical position of the slice corresponding to pixel coordinates to the position in the 3D reconstructed world coordinate system. (Subscript) Used to identify the total number of slices, subscript Used to identify physical density.

[0095] PSF is the point spread function. Indicates according to the first The point spread function is determined by the in-plane pixel spacing, slice thickness, and spatial orientation of each slice. The initial slice affine matrix is ​​used to establish the initial coordinate mapping. The final spatial transformation serves as the current absolute coordinate mapping for subsequent steps and is not superimposed on the initial slice affine matrix. Physical density map. The larger the value, the more sufficient the slice observation support for the corresponding three-dimensional location; physical density map The smaller the value, the more likely the corresponding three-dimensional location is to be in an under-observed region.

[0096] Furthermore, based on the rough volume obtained in the last round... and physical density map Generate density-gated geometric prior volumes.

[0097] Specifically, the physical density map is first converted into observation confidence scores. Then, the coarse volume and physical density map are combined by channel and input into the pre-trained residual repair network. ; Calculate the gating function based on the observation confidence level The residual repair strength is adjusted using a gating function, and the gated residual is added to the coarsely estimated volume to obtain the geometric prior volume. The formulas for calculating the observation confidence level, gating function, and geometric prior volume are expressed as follows:

[0098] ;

[0099] ;

[0100] ;

[0101] in, This indicates a complete rough estimate of the volume. This indicates its intensity at position x; Represents the complete geometric prior volume. This indicates its intensity at position x. This represents the complete physical density map. This represents the value of the physical density map at position x in the 3D reconstructed world coordinate system. This represents an exponential function with base e. The parameter is A pre-trained residual repair network; and Indicates the preset gating coefficient, and .

[0102] When the observation confidence is high, the gating function reduces the modification of the coarse volume by the residual repair network to preserve the details provided by the input observation slices; when the observation confidence is low, the gating function enhances the repair effect of the residual repair network to complete the anatomical structure of the under-observed regions. The resulting geometric prior volume... It also serves as the basis for Gaussian initialization, the prefitting target, and the prior distillation target.

[0103] Step S4: Initialize the three-dimensional Gaussian primitives based on geometric prior volume to obtain the initial three-dimensional Gaussian field.

[0104] Specifically, effective voxels are selected in the foreground region of the geometric prior volume according to the intensity threshold. The coordinates of the effective voxels are transformed to the 3D reconstruction world coordinate system, and the center position of each 3D Gaussian primitive is obtained based on the transformed coordinates. The intensity parameters of each 3D Gaussian primitive are initialized based on the corresponding voxel intensity. Simultaneously initialize the scaling parameters of each 3D Gaussian primitive. and the rotation parameters used to generate the rotation matrix, and convert the rotation parameters into the rotation matrix. And construct a scale matrix based on the scale parameters. This yields a set of three-dimensional Gaussian primitives. Represented as:

[0105] ;

[0106] ;

[0107] ;

[0108] in, Indicates the number of three-dimensional Gaussian primitives. Represents a three-dimensional Gaussian primitive index. Indicates the first The covariance matrix of a three-dimensional Gaussian primitive. This represents the 3×3 rotation matrix obtained by transforming the rotation parameters of the j-th 3D Gaussian primitive. Let represent the diagonal scaling matrix of the j-th 3D Gaussian primitive, and diag(·) denotes the operation of constructing a diagonal matrix from the listed elements. , and Let T represent the scale components of the j-th 3D Gaussian primitive along the three coordinate axes, and T denote the transpose of the matrix or vector. Since the center and intensity of the 3D Gaussian primitive are derived from the geometric prior volume, the initial 3D Gaussian field has a stable overall spatial distribution, providing a structural basis for subsequent optimization.

[0109] Furthermore, based on the geometric prior volume and the initial three-dimensional Gaussian field, the first stage of prior volume fitting is performed to obtain the prefitted three-dimensional Gaussian field.

[0110] Specifically, three-dimensional points are sampled in the foreground region of the geometric prior volume, and the initial three-dimensional Gaussian field is directly queried in the three-dimensional reconstructed world coordinate system to obtain the Gaussian predicted intensity. And predict the intensity using Gaussian. With geometric prior volume The difference between them constructs the volume fitting loss. The volume fitting loss is expressed as:

[0111] ;

[0112] ;

[0113] in, The foreground region representing the geometric prior volume. This indicates the number of sampling points participating in the calculation within the foreground region. Indicates the first A scale vector of a three-dimensional Gaussian primitive. This represents the preset target scale vector. This is used to constrain the scale of each 3D Gaussian primitive to be close to the target scale. Indicates the scale regularization weight. The L2 norm is represented. The initial 3D Gaussian field is optimized to a prefitted 3D Gaussian field consistent with the geometric prior volume, reducing the risk of random drift, excessive scaling, or excessive expansion of the 3D Gaussian primitives.

[0114] Step S5: Based on the input observed slice, slice thickness, pixel spacing, and the spatial transformation obtained in the last round. In addition, a three-dimensional Gaussian field is prefitted to simulate the two-dimensional slice imaging process, resulting in predicted slices. Based on the intensity difference between the predicted slices and the input observed slices, a data consistency loss is constructed.

[0115] Specifically, with As the first The initial values ​​of each slice pose are introduced, and the residual rigidity transformation to be optimized is introduced. The residual rigid transformation is defined in the 3D reconstructed world coordinate system and rotated around the center of the corresponding slice. It is applied to the 3D query position obtained from the final spatial transformation to obtain the current corrected spatial transformation. For the first Pixel coordinates in a slice ,pass Obtain its 3D query position in the 3D reconstructed world coordinate system.

[0116] According to the The thickness of each slice and the in-plane pixel spacing generate the point spread function covariance in the slice coordinate system. and will the Covariance of a three-dimensional Gaussian primitive With the rotation matrix of the current slice The equivalent covariance under slice observations is obtained by analytically superimposing the covariances of the transformed point spread function. :

[0117] ;

[0118] ;

[0119] In the formula, the superscript res denotes the residual rigid transformation, loc denotes the local coordinate system of the slice, and obs denotes the observation equivalent covariance after considering the point spread function. "" indicates the composition of rigid spatial transformations, and the composition order is to first apply the final spatial transformation, and then apply the residual rigid transformation.

[0120] Based on equivalent covariance, three-dimensional Gaussian primitives within the neighborhood of the three-dimensional query location are selected from the prefitted three-dimensional Gaussian field, and the calculation of each three-dimensional Gaussian primitive at the 1st... slice pixel coordinates Analysis weight at the location The analytical weights are then normalized to obtain the predicted intensity. Arrange all predicted intensities within the slice pixel domain according to their original pixel positions to obtain the first... 1. Predicted slices; construct a data consistency loss based on the intensity difference between the predicted slices and the input observed slices. :

[0121] ;

[0122] ;

[0123] ;

[0124] in, express The rotating part, Indicates distance from the 3D query location Recent A set of three-dimensional Gaussian primitives, This represents the number of nearest-neighbor 3D Gaussian primitives. This represents a preset positive number used to ensure numerical stability. Indicates the first Intensity scaling factor for each slice, Indicates the first One predicted slice, Indicates the first One input observation slice; The superscript indicates the L1 norm calculated over the slice pixel domain. This represents matrix inversion. The image intensity of the input observation slice is not spatially resampled; the currently corrected spatial transformation is only used to determine the 3D query location corresponding to its pixels. By... The predicted intensity is calculated for each pixel position of the input observation slice, and all predicted intensities are arranged according to their original pixel positions to obtain the predicted intensity of the nth slice. One predicted slice; prediction slice and data consistency loss. Slice observation constraints for joint optimization.

[0125] Step S6, based on geometric prior volume Prefitting a 3D Gaussian field and data consistency loss The second stage of joint optimization is performed and the three-dimensional reconstruction volume is output.

[0126] Specifically, three-dimensional points are sampled in the three-dimensional reconstructed world coordinate system, and the predicted volume of the current three-dimensional Gaussian field is calculated. With geometric prior volume Prior distillation loss between Furthermore, the a priori distillation loss, data consistency loss, and scaling regularization term are combined to obtain the joint loss. :

[0127] ;

[0128] ;

[0129] in, Indicates the first Prior distillation weights in the next iteration; This represents the set of predicted intensities of the current 3D Gaussian field at the sampled 3D location. This represents the set of target intensities at the same three-dimensional location for geometrically prior volumes. This represents the point-by-point intensity difference between the two at the corresponding sampling locations. The L1 norm is calculated at three-dimensional sampling points, and the subscript is used. Used to identify prior distillation losses Used to identify joint losses centered on slice observation constraints.

[0130] According to the preset iteration interval, make The initial weights decay linearly to the final weights, ensuring that the early optimization phase prioritizes preserving the global structure provided by the geometric prior, while the later optimization phase focuses on fitting the input observation slices. This is based on joint loss. The center position, intensity, scale, and rotation parameters of the three-dimensional Gaussian primitive, as well as the residual motion parameters of each slice, are updated together to obtain the final three-dimensional Gaussian field. Then, the intensity of the final three-dimensional Gaussian field is calculated on the target three-dimensional mesh to obtain the high-resolution three-dimensional fetal brain magnetic resonance reconstruction volume.

[0131] The point spread function is modeled using a zero-mean anisotropic 3D Gaussian kernel. Its covariance in the slice coordinate system is determined by the pixel spacing between the two planes and the slice thickness, and is transformed to the 3D reconstructed world coordinate system according to the rotation part of the corresponding slice space transformation. Based on the property that the covariances are added after convolution of the zero-mean Gaussian function, the covariance of the point spread function in the 3D reconstructed world coordinate system is analytically added to the covariance of the 3D Gaussian primitive to obtain the equivalent covariance.

[0132] The 3D Gaussian primitive is determined by its center position, intensity, scale, and rotation parameters. In the prior volume fitting and simulated slice imaging process, instead of projecting the 3D Gaussian primitive onto a 2D imaging plane and then rasterizing it, the contribution of the 3D Gaussian primitive to the 3D query location is directly calculated in the reconstructed 3D world coordinate system. For the 3D query location, a preset number of 3D Gaussian primitives closest to the 3D query location are selected through nearest neighbor retrieval. Spatial weights are calculated for each primitive, and then normalized weighted to obtain the intensity of the 3D Gaussian field at the 3D query location.

[0133]

[0134]

[0135] in, This represents the unnormalized spatial weight of the j-th 3D Gaussian primitive at the 3D query position x. Represents the closest to x A set of three-dimensional Gaussian primitives; the three-dimensional query location includes three-dimensional sampling points in the geometric prior volume, target three-dimensional mesh points, or slice pixel locations mapped to the three-dimensional reconstructed world coordinate system by the current corrected spatial transformation. By only calculating the contribution of neighboring three-dimensional Gaussian primitives and omitting the two-dimensional projection and rasterization processes, the computational cost of three-dimensional Gaussian field query and slice imaging simulation is reduced.

[0136] The slice-to-volume registration network and the residual repair network constitute the prior learning network. The prior learning network is pre-trained using a stack of two-dimensional slices obtained from a high-quality three-dimensional fetal brain magnetic resonance volume simulation, the corresponding real space transformation, and a high-quality three-dimensional volume. After training, the network parameters are fixed for forward inference.

[0137] The following specific embodiments further illustrate the present invention's method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors. The overall process is as follows: Figure 2 As shown. The operating environment uses an NVIDIA RTX 4090 graphics processor with 24 GB of video memory, and the specific implementation process is as follows.

[0138] Before reconstructing the object to be reconstructed, a high-quality fetal brain magnetic resonance imaging (MRI) volumetric simulation of a two-dimensional slice stack was used to supervise the training of the slice-to-volume registration network and the residual repair network. The simulation incorporated random rigid motion, different sampling directions, variations in slice thickness and interval, and slice intensity inhomogeneity, while retaining realistic spatial transformations and the original high-quality three-dimensional volume as supervisory information. During training, the slice-to-volume registration network was supervised by realistic spatial transformations, and the estimated volume and geometric prior volume in each round were supervised by high-quality three-dimensional volume. The network parameters were updated by minimizing spatial transformation errors and volume reconstruction errors. After training, the network parameters were fixed; only forward inference was performed for each object to be reconstructed, without retraining the network.

[0139] Prepare the input data and establish a 3D reconstructed world coordinate system. This embodiment uses two types of data: The first type is a stack of slices simulated from high-quality 3D fetal brain atlases from the Computational Radiology Laboratory (CRL) fetal brain atlas and the Fetal Tissue Annotation and Segmentation Dataset (FeTA) 2.2, with a gestational age range of 21 to 38 weeks. Each object contains three approximately orthogonal stacks: axial, coronal, and sagittal, with a slice resolution of 0.8 × 0.8 × 2.2 mm³. The second type is T2-weighted single-shot fast spin echo data of 90 fetal brains acquired using a 3TP Philips Ingenia MRI scanner, with a gestational age range of 28 to 37 weeks, an in-plane resolution of 0.71 × 0.71 mm², and a slice thickness of 3.0 mm. The input file is in NIfTI format, and the corresponding affine matrix and fetal brain mask are read.

[0140] For each stack, the out-of-mask intensity and negative intensity are set to zero. If no mask is provided, an initial mask is generated for regions with image intensity greater than 0.01, and the mask is moderately expanded using a Gaussian filter with a standard deviation of 0.5. The 99.9th percentile of the foreground intensity of all stacks is used as the upper cutoff, and the intensity is then normalized to [0,1]. Effective pixels are transformed to the 3D reconstruction world coordinate system based on the slice affine matrix, and their coordinate range is expanded to 1.1 times the original range as the reconstruction bounding box. A target 3D mesh is established with an isotropic voxel spacing of 0.8 mm. An anisotropic Gaussian point spread function is established based on the in-plane pixel spacing and slice thickness of each stack.

[0141] like Figure 3 As shown, the process involves alternating iterative slice transformation updates and volume estimation. The initial spatial transformation for each slice is set to a unit transformation, and the network iterates four times in one forward inference. In the first round, the spatial transformation and slice quality weights are estimated based on the input observed slice and its location information. In subsequent rounds, the estimated volume from the previous round is sampled onto the corresponding 2D pixel grid of each input observed slice, based on the spatial transformation from the previous round, resulting in a simulated slice with the same spatial location and size as the corresponding input observed slice. Then, the input observed slice, the simulated slice, and the current location information are input into the registration network to update the spatial transformation and slice quality weights, followed by super-resolution volume estimation based on the point spread function. The output of the fourth round serves as the final spatial transformation and coarse volume estimate.

[0142] The coarse volume was resampled to a 0.8 mm isotropic grid. The mean and standard deviation of the coarse volume foreground and the input observation slice foreground were calculated separately. A linear transformation was applied to make their intensity distributions consistent, and negative values ​​were truncated to zero. The final spatial transformation was used for subsequent density map construction and 3D coordinate lookup of slice pixels. The intensity data of the input observation slice was not spatially resampled again.

[0143] like Figure 4 As shown, a physical density map is constructed. For each input observation slice, a unit intensity slice of the same size with a pixel value of 1 is created. Backprojection and accumulation are performed using the final spatial transformation, point spread function, and target 3D mesh, but without intensity equalization between slices, to obtain the physical density map. The physical density is then converted into observation confidence.

[0144] like Figure 4 As shown, a geometric prior volume is generated. The coarsely estimated volume and physical density map after intensity matching are used as two input channels and fed into a 3D residual encoder-decoder to output the residual volume, as shown. Figure 5 As shown in the figure. In this embodiment, the density gating coefficients α and β are set to 0.05 and 1.0, respectively; when the observation confidence level approaches 1, the residual repair magnitude approaches 5% of the original residual; when the observation confidence level approaches 0, the full residual repair magnitude is used; for other positions, the magnitude is continuously adjusted between the two according to the observation confidence level. The gated residual volume is added to the coarsely estimated volume voxel by voxel to obtain the geometric prior volume.

[0145] The 3D Gaussian primitives are initialized using geometric prior volume. Foreground voxels with an intensity greater than 5% of the maximum intensity of the geometric prior volume are selected, their voxel centers are transformed to the 3D reconstructed world coordinate system, and 80,000 positions are randomly sampled from these voxels as Gaussian centers. Sampling with replacement is used when the number of foreground voxels is insufficient. The Gaussian intensity is initialized with the corresponding voxel intensity, the scale in all three directions is initialized to 1.5 mm, and the rotation quaternion is initialized to a unit rotation.

[0146] The first stage involves fitting the prior volume. Voxels with an intensity greater than 1% of the maximum intensity within the geometric prior volume are used as sampling regions. In each iteration, 8192 voxel centers are randomly sampled and transformed to the 3D reconstructed world coordinate system. For each 3D query location, the 50 nearest 3D Gaussian primitives are retrieved, and the predicted Gaussian field intensity is calculated. 201 optimization iterations are performed using the mean squared error between the predicted intensity and the geometric prior volume intensity, along with a scale regularization term. The target scale is set to approximately 1.6 mm, and the scale regularization weight is set to 0.01. During optimization, the gradient norm is clipped to 1.0, and the Gaussian intensity is constrained to non-negative values, resulting in a pre-fitted 3D Gaussian field.

[0147] The second stage involves fitting the input observation slices. The residual rotation of each slice is initialized to a unit rotation, and the residual translation is initialized to zero. The 3D query position of the slice pixels is updated based on the current slice pose, and the corresponding point spread function covariance is rotated. The equivalent covariance after convolving the 3D Gaussian primitive with the Gaussian point spread function is:

[0148] ;

[0149] in, This represents the covariance of the local point spread function of the k-th slice after transformation by the current slice rotation matrix, in the 3D reconstructed world coordinate system. To reduce the number of 3D Gaussian primitives involved in the calculation for each 3D query location, this embodiment employs a nearest neighbor retrieval method based on Euclidean distance. A nearest neighbor index is established for the center position of each 3D Gaussian primitive, and the nearest neighbor retrieval is implemented on the graphics processor using the FAISS vector similarity retrieval library. Only the 50 nearest 3D Gaussian primitives are queried for each slice pixel, and the analytical weights and prediction strengths are calculated based on the equivalent covariance.

[0150] The above calculation is repeated for all pixels of the same input observation slice, and the resulting predicted intensities are arranged according to their original pixel positions to obtain a predicted slice with the same size as the input observation slice; the nearest neighbor index is rebuilt every 20 optimization iterations. The L1 data consistency loss is calculated between the predicted slice and the input observation slice with the same pixel position. To accommodate the intensity differences between different slices, this embodiment also optimizes the slice intensity scaling parameter.

[0151] A priori distillation constraint is incorporated during the slice fitting stage. In each iteration, 4096 3D locations are uniformly sampled within the reconstructed bounding box. The target intensity is obtained using trilinear interpolation within the geometric prior volume, and only locations with a target intensity greater than 0.01 are retained. The current 3D Gaussian field is queried at the same location, and the L1 difference between the two is used as the priori distillation loss. In this embodiment, the initial priori distillation weights are maintained before the preset start iteration position, the weights are linearly decayed to the termination weight between the start iteration position and the preset end iteration position, and the termination weight is maintained after the end iteration position.

[0152] The data consistency loss, scale regularization term, and weighted prior distillation loss were combined into a joint loss, and the AdamW optimizer was used to perform 600 joint optimizations. The initial learning rates for Gaussian center and scale were set to 2.5 × 10⁻², for Gaussian rotation and intensity to 1.0 × 10⁻², and for slice residual rotation and translation to 1.0 × 10⁻³ and 1.0 × 10⁻¹, respectively; the initial learning rate for slice intensity scaling parameters was set to 1.0 × 10⁻³. Every 200 iterations, each learning rate was multiplied by 0.5.

[0153] After joint optimization, the final three-dimensional Gaussian field is queried point by point on the 0.8 mm isotropic target three-dimensional mesh. For each mesh location, 50 neighboring Gaussian primitives are selected for normalization and weighting. The query results are then combined with the target mesh affine matrix and saved as the fetal brain magnetic resonance three-dimensional reconstruction volume in NIfTI format.

[0154] Experimental verification was conducted using the above parameters. On simulated data, the average reconstruction time of our method was approximately 90 s, with a peak signal-to-noise ratio (PSNR) of 24.56 ± 2.87 dB and a structural similarity of 0.905 ± 0.033. The PSNR and structural similarity of the 3D Gaussian primitive reconstruction method without geometric priors were 24.40 ± 2.93 dB and 0.898 ± 0.036, respectively. In single-slice stack stress tests, the PSNR of our method was 22.64 dB, an improvement of 1.87 dB compared to the method without geometric priors. After removing the prior distillation constraint, the PSNR decreased by 1.16 dB. These results demonstrate that density-gated geometric priors and prior distillation can improve reconstruction stability under conditions of low quality or insufficient effective observations.

[0155] In summary, this invention describes the sufficiency of observation at each location in the three-dimensional reconstructed world coordinate system through a physical density map, thus linking the generation process of geometric priors with the physical process of fetal brain magnetic resonance imaging slice acquisition, and is able to distinguish between areas with sufficient observation and areas with insufficient observation.

[0156] This invention initializes three-dimensional Gaussian primitives with density-gated geometric prior volume, enabling the Gaussian primitives to have a more stable overall anatomical structure at the start of optimization, thereby reducing the possibility of structural distortion or local collapse of the Gaussian primitives under low-quality input conditions.

[0157] This invention employs a two-stage optimization approach: prior volume fitting and input observation slice fitting. First, a stable three-dimensional structure is established based on the geometric prior volume, and then image details are restored based on the input observation slices, thereby balancing the stability of the reconstructed structure and the ability to restore local details.

[0158] This invention utilizes the analytical covariance superposition relationship between three-dimensional Gaussian primitives and Gaussian point spread functions, and directly queries neighboring three-dimensional Gaussian primitives in the three-dimensional reconstruction world coordinate system, reducing the amount of random sampling, two-dimensional projection and rasterization calculations, which helps to maintain the reconstruction speed.

[0159] This invention introduces prior distillation constraints in the input observation slice fitting stage, so that the three-dimensional Gaussian field is subject to geometric prior constraints while fitting the intensity of the input observation slice, thereby improving the robustness of the reconstruction results in cases such as significant fetal movement, poor slice quality, or insufficient effective observation.

[0160] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit disclosed in the present invention should fall within the patent scope covered by the present invention.

Claims

1. A method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors, characterized in that, Includes the following steps: Obtain the stack of two-dimensional slices from fetal brain magnetic resonance imaging (MRI), preprocess the stack of two-dimensional slices from fetal brain MRI, and obtain the input observation slice dataset; Based on the input observation slice dataset, the slice spatial transformation and estimated volume are updated alternately to obtain the final spatial transformation and coarse volume of each slice; Based on the input observation slice dataset and the final spatial transformation of the slice, a physical density map is constructed. Based on the coarse volume estimate and the physical density map, a geometric prior volume is generated through density-gated residual repair. The three-dimensional Gaussian primitives are initialized based on the geometric prior volume to obtain the initial three-dimensional Gaussian field. Based on the geometric prior volume and the initial three-dimensional Gaussian field, the prior volume is fitted to obtain the prefitted three-dimensional Gaussian field. Based on the input observation slice dataset, the final spatial transformation, and the prefitted 3D Gaussian field, the slice imaging process is simulated to obtain the predicted slice. Based on the intensity difference between the predicted slice and the input observation slice, a data consistency loss is constructed. Based on the geometric prior volume, the prefitted 3D Gaussian field, and the data consistency loss, the 3D Gaussian primitives are updated to obtain the final 3D Gaussian field. Based on the final 3D Gaussian field, the 3D reconstructed volume of the fetal brain magnetic resonance imaging is output.

2. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 1, characterized in that, Obtain the stack of two-dimensional fetal brain magnetic resonance imaging (MRI) slices, preprocess the stack of fetal brain MRI slices to obtain the input observation slice dataset, specifically: The fetal brain magnetic resonance imaging (MRI) two-dimensional slice stack and its acquisition parameters are obtained. The two-dimensional slice stack is then processed by image reading, brain region mask acquisition, invalid background removal, intensity truncation and intensity normalization. Based on the initial affine matrix of each slice, the homogeneous pixel coordinates of the effective pixels are converted into initial world coordinates to obtain the input observation slice dataset. The input observation slice dataset includes the intensity of the input observation slice image after intensity preprocessing but without spatial resampling, homogeneous pixel coordinates, initial slice spatial coordinates, initial slice affine matrix, slice thickness, pixel spacing, and slice center coordinates, which serve as the unified input for subsequent slice registration, physical density calculation, and 3D Gaussian query.

3. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 2, characterized in that, Based on the input observation slice dataset, the slice spatial transformation and estimated volume are updated alternately to obtain the final spatial transformation and coarse volume estimate for each slice, specifically: Initialize the nine-dimensional spatial transformation representation of each slice, and do not use the volume estimated in the previous round in the first iteration; In the In the round of iteration, the first step is based on the input observation slice. Subsequent rounds are based on the input observation slice, the spatial transformation of the previous round, and the simulated slice generated by the estimated volume of the previous round. The nine-dimensional spatial transformation residual parameters of each slice are predicted through the slice-to-volume registration network. The residual parameters are added element by element to the nine-dimensional spatial transformation representation of the previous round, and the updated nine-dimensional spatial transformation representation is converted into the rigid spatial transformation of the current round. The second step involves performing point spread function back projection and super-resolution reconstruction on the input observation slices based on the updated spatial transformation to obtain the estimated volume for this round. The updated spatial transformation and estimated volume are then passed to the next iteration to progressively improve the accuracy of slice registration and volume estimation. The spatial transformation obtained in the final iteration serves as the final spatial transformation of each slice relative to the 3D reconstructed world coordinate system. The estimated volume obtained in the final round before density-gated residual repair is used as the final round coarse volume estimate. .

4. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 3, characterized in that, Based on the input observation slice dataset and the final spatial transformation of the slices, a physical density map is constructed, specifically as follows: The point spread function during the slicing acquisition process is modeled as a Gaussian point spread function, and then subjected to the final spatial transformation. The point spread function contributions of all input observation slices are accumulated to obtain the physical density map. Its calculation formula is expressed as: ； in, This indicates the position in the 3D reconstructed world coordinate system. This indicates the total number of observed slices. Indicates the first The pixel field of each slice Represents the pixel coordinates of the slice. Indicates the first The final pose of each slice determines the local physical position of the slice corresponding to the pixel coordinates and maps it to the position in the 3D reconstructed world coordinate system. Indicates according to the first The point spread function is determined by the in-plane pixel spacing, slice thickness and spatial orientation of each slice; The initial slice affine matrix is ​​used to establish the initial coordinate mapping. The final spatial transformation serves as the current absolute coordinate mapping used in subsequent steps and is not superimposed on the initial slice affine matrix. The physical density map is used to represent the degree to which each location in the 3D reconstructed world coordinate system is covered by the input observation slice.

5. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 4, characterized in that, Based on the coarsely estimated volume and physical density map, a geometric prior volume is generated through density-gated residual repair, specifically: First, convert the physical density map into observation confidence scores. Then, the coarse volume and physical density map are combined by channel and input into the pre-trained residual repair network. ; Calculate the gate function based on the observation confidence level. The residual repair strength is adjusted using a gating function, and the gated residual is added to the coarsely estimated volume to obtain the geometric prior volume. ; The formulas for calculating the observation confidence level, the gating function, and the geometric prior volume are expressed as follows: ； ； ； in, This indicates a complete rough estimate of the volume. Represents the complete physical density map. This represents an exponential function with the natural constant e as its base. and Indicates the preset gating coefficient, and .

6. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 5, characterized in that, The initial three-dimensional Gaussian field is obtained by initializing the three-dimensional Gaussian primitives based on geometric prior volume, specifically: Effective voxels are selected in the foreground region of the geometric prior volume according to the intensity threshold. The coordinates of the effective voxels are transformed to the 3D reconstructed world coordinate system, and the center position of each 3D Gaussian primitive is obtained by sampling based on the transformed coordinates. ; The intensity parameters of each 3D Gaussian primitive are initialized based on the corresponding voxel intensity. Simultaneously initialize the scaling parameters of each 3D Gaussian primitive. and the rotation parameters used to generate the rotation matrix, and convert the rotation parameters into the rotation matrix. And construct a scale matrix based on the scale parameters; The resulting set of three-dimensional Gaussian primitives Represented as: ； ； ； in, Indicates the number of three-dimensional Gaussian primitives. Indicates the first The covariance matrix of a three-dimensional Gaussian primitive. This represents the 3×3 rotation matrix obtained by transforming the rotation parameters of the j-th 3D Gaussian primitive. Let represent the diagonal scaling matrix of the j-th 3D Gaussian primitive, and diag(·) denotes the operation of constructing a diagonal matrix from the listed elements. , and These represent the scale components of the j-th three-dimensional Gaussian primitive along the three coordinate axes, respectively.

7. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 6, characterized in that, Based on the geometric prior volume and the initial three-dimensional Gaussian field, a prior volume fitting is performed to obtain the prefitted three-dimensional Gaussian field, specifically: Three-dimensional points are sampled in the foreground region of the geometric prior volume, and the initial three-dimensional Gaussian field is directly queried in the three-dimensional reconstructed world coordinate system to obtain the Gaussian predicted intensity. And predict the intensity using Gaussian. With geometric prior volume The difference between them constructs the volume fitting loss. The volume fitting loss is expressed as: ； ； in, The foreground region representing the geometric prior volume. Indicates the first A scale vector of a three-dimensional Gaussian primitive. This represents the preset target scale vector. This is used to constrain the scale of each 3D Gaussian primitive to be close to the target scale. Indicates the scale regularization weight. This represents the L2 norm.

8. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 7, characterized in that, Based on the input observation slice dataset, the final spatial transformation, and the prefitted 3D Gaussian field, the slice imaging process is simulated to obtain predicted slices. A data consistency loss is constructed based on the intensity difference between the predicted slices and the input observation slices, specifically: by As the first The initial values ​​of each slice pose are introduced, and the residual rigidity transformation to be optimized is introduced. ; The residual rigid transformation is defined in the 3D reconstructed world coordinate system and rotated around the center of the corresponding slice. It is then applied to the 3D query position obtained from the final spatial transformation to obtain the current corrected spatial transformation. ; For the Pixel coordinates in a slice ,pass Obtain its 3D query position in the 3D reconstructed world coordinate system; according to the first The thickness of each slice and the in-plane pixel spacing generate the point spread function covariance in the slice coordinate system. and will the Covariance of a three-dimensional Gaussian primitive With the rotation matrix of the current slice The equivalent covariance under slice observations is obtained by analytically superimposing the covariances of the transformed point spread function. : ； ； In the formula, the symbol " " indicates the composition of rigid spatial transformations, with the composition order being to apply the final spatial transformation first, followed by the residual rigid transformation; Based on equivalent covariance, three-dimensional Gaussian primitives within the neighborhood of the three-dimensional query location are selected from the prefitted three-dimensional Gaussian field, and the calculation of each three-dimensional Gaussian primitive at the 1st... slice pixel coordinates Analysis weight at the location The analytical weights are then normalized to obtain the predicted intensity. Arrange all predicted intensities within the slice pixel domain according to their original pixel positions to obtain the first...

1. Predict a slice; construct a data consistency loss based on the intensity difference between the predicted slice and the input observed slice. : ； ； ； in, express The rotating part, Indicates distance from the 3D query location Recent A set of three-dimensional Gaussian primitives, This represents the number of nearest-neighbor 3D Gaussian primitives. This represents a preset positive number used to ensure numerical stability. Indicates the first Intensity scaling factor for each slice, This represents the k-th predicted slice. Indicates the first One input observation slice, This represents the L1 norm calculated over the slice pixel domain.

9. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 8, characterized in that, Based on the geometric prior volume, the prefitted 3D Gaussian field, and the data consistency loss, the 3D Gaussian primitives are updated to obtain the final 3D Gaussian field. Based on the final 3D Gaussian field, the 3D reconstructed volume of the fetal brain magnetic resonance imaging is output, specifically: Sample 3D points in the reconstructed 3D world coordinate system and calculate the predicted volume of the current 3D Gaussian field. With geometric prior volume Prior distillation loss between Furthermore, the a priori distillation loss, data consistency loss, and scaling regularization term are combined to obtain the joint loss. : ； ； in, Indicates the first Prior distillation weights in the next iteration; according to the preset iteration interval, make The initial weights are linearly decayed to the final weights, so that the early optimization focuses on maintaining the global structure provided by the geometric prior, and the later optimization focuses on fitting the input observation slices. Based on joint loss The center position, intensity, scale, and rotation parameters of the three-dimensional Gaussian primitive, as well as the residual motion parameters of each slice, are updated together to obtain the final three-dimensional Gaussian field. Then, the intensity of the final three-dimensional Gaussian field is calculated on the target three-dimensional mesh to obtain the high-resolution three-dimensional fetal brain magnetic resonance reconstruction volume.

10. The method for three-dimensional reconstruction of fetal brain magnetic resonance imaging based on density-gated geometric priors according to claim 9, characterized in that, The 3D Gaussian primitive is determined by the center position, intensity, scale, and rotation parameters. The prior volume fitting and simulated slice imaging process does not use the method of rasterizing the 3D Gaussian primitive after projecting it onto the 2D imaging plane. Instead, it directly calculates the contribution of the 3D Gaussian primitive to the 3D query position in the 3D reconstructed world coordinate system. For the 3D query location, a preset number of 3D Gaussian primitives closest to the 3D query location are selected through nearest neighbor retrieval. Spatial weights are calculated for each primitive and then normalized and weighted to obtain the intensity of the 3D Gaussian field at the 3D query location. ； ； in, This represents the unnormalized spatial weight of the j-th 3D Gaussian primitive at the 3D query position x. Represents the closest to x A set of three-dimensional Gaussian primitives; the three-dimensional query location includes three-dimensional sampling points in the geometric prior volume, target three-dimensional mesh points, or slice pixel locations mapped to the three-dimensional reconstructed world coordinate system by the current corrected spatial transformation.

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