A method for detail enhancement reconstruction of a geotechnical medium CT image

Abstract

This invention discloses a method for detail enhancement and reconstruction of CT images of soil and rock media. The method includes the following steps: acquiring and preprocessing CT projection data of the soil and rock media; representing the soil and rock media to be reconstructed as a superposition of N three-dimensional Gaussian elements and performing three-dimensional Gaussian initialization; introducing a detail-sensitive modulation factor into the Gaussian splash model; during the densification training phase, if the detail-sensitive modulation factor is greater than a preset sensitivity threshold, it is considered a region with significant detail; performing a splitting operation on the Gaussian elements of the region with significant detail according to a set splitting iteration node; obtaining the trained Gaussian splash model through iterative optimization; the trained Gaussian splash model is used for subsequent CT reconstruction of the soil and rock media, outputting the predicted projection and the corresponding predicted density and covariance matrix of Gaussian elements in the soil and rock media. The introduction of a detail-sensitive weight modulation mechanism and edge constraint loss into the Gaussian splash model achieves high-precision reconstruction of the fine internal structure of the soil and rock media.

Description

Technical Field

[0001] This invention discloses a method for enhancing the details of 3D reconstruction of CT images of soil and rock media, belonging to the field of industrial CT image reconstruction and digital rock core characterization technology. Background Technology

[0002] Industrial CT 3D reconstruction is a core technology for digital core characterization. Traditional iterative algorithms such as FDK and SART struggle to accurately reconstruct micron-level fine structures in rocks / soils, such as micropores, microcracks, and fine-grained mineral boundaries, under conditions of insufficient projection numbers and low signal-to-noise ratio. This often results in problems like blurred boundaries, amplified noise, and missed detections of weak absorbing phases. Currently, Gaussian sputtering (R... 2 While the Gaussian sputtering CT (GS) reconstruction method achieves efficient optimization through 3D Gaussian element modeling, it still suffers from key drawbacks: isotropic Gaussian element modeling cannot adapt to directional structures such as fractures and lamellar structures, is insensitive to low-contrast facies interfaces, and lacks sufficient spatial representation of fine materials, exhibiting a significant voxel averaging effect. These problems severely restrict the accuracy of pore network analysis and fracture identification in complex rock samples such as shale and sandstone. Therefore, there is an urgent need to develop a Gaussian sputtering CT reconstruction method that can enhance the identification of fine materials and maintain the integrity of microscopic boundaries to meet the industrial demands for high-precision digital core characterization.

[0003] Traditional rock CT reconstruction typically employs FDK, SART, SIRT, or voxel-based iterative algorithms. However, these algorithms are prone to problems such as blurred boundaries, amplified noise, and loss of detail when dealing with insufficient projection numbers, low signal-to-noise ratios, and small-scale minerals, pores, and fractures. In recent years, with the development of deep learning, researchers need to propose effective methods for CT reconstruction, such as the R... 2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction. This method introduces 3D Gaussian splashing into sparse-view CT reconstruction, improving reconstruction accuracy and efficiency by correcting integral biases in the X-ray projection process. Li et al. proposed 3DGR-CT: Sparse-ViewCT Reconstruction with a 3D Gaussian Representation. This method utilizes FBP images to guide Gaussian initialization and combines it with a differentiable CT projector for sparse-view CT reconstruction. The above methods are mainly aimed at medical CT images and do not establish specific detail saliency evaluation, residual-guided modulation, and directional Gaussian splitting mechanisms for fine structures such as micropores, fine-grained mineral boundaries, and weakly absorbing phases in rock CT. Therefore, existing Gaussian splashing reconstruction methods still have the following shortcomings in rock scenes: first, insufficient representation of fine materials; second, insensitivity to low-contrast interfaces; and third, insufficient adaptation to complex anisotropic structures.

[0004] Therefore, this invention proposes an improved Gaussian splash reconstruction method with enhanced detail material. The core idea is to introduce a multi-scale, anisotropic, detail-guided, and adaptively multiplying Gaussian field modeling approach based on the original 3D Gaussian representation, thereby improving the model's ability to analyze fine structures while maintaining high reconstruction efficiency. Summary of the Invention

[0005] To address the shortcomings of existing Gaussian splashing methods in representing fine materials, micropores, microcracks, fine-grained mineral boundaries, and low-contrast phase interfaces in CT reconstruction of soil and rock media, this invention aims to provide a fine material-enhanced Gaussian splashing CT reconstruction method for soil and rock media. This method introduces a detail-sensitive weight modulation mechanism and edge constraint loss into the Gaussian splashing model to achieve high-precision reconstruction of the fine structure inside the soil and rock media.

[0006] The technical solution adopted by the present invention to solve the aforementioned technical problem is as follows: A CT reconstruction method for soil and rock media based on fine material enhancement and Gaussian splashing, the method comprising the following: Acquire and preprocess CT projection data of soil and rock media; The soil and rock medium to be reconstructed is represented as a superposition of N three-dimensional Gaussian elements, and three-dimensional Gaussian initialization is performed; A detail-sensitive modulation factor is introduced into the Gaussian splash model. During the densification training phase, if the detail-sensitive modulation factor is greater than a preset sensitivity threshold, it is considered a salient region. Gaussian cells in the salient region are split according to a set splitting iteration node. The trained Gaussian splash model is obtained through iterative optimization. The trained Gaussian splash model is used for subsequent CT reconstruction of soil and rock media, outputting the predicted projection and the corresponding Gaussian element predicted density and Gaussian element covariance matrix of the soil and rock media.

[0007] Furthermore, the detail-sensitive modulation factor is determined based on a weighted sum of a detail saliency index and a residual response intensity; the detail saliency index is determined by a weighted sum of the local first-order gradient magnitude, Frobenius norm, and average reprojection error of each Gaussian element; and the residual response intensity is obtained by a weighted average of the projection residuals in the ray set affected by each Gaussian element.

[0008] During training, the loss function is a composite loss function consisting of the weighted sum of the L1 loss of the projected image, the structural similarity loss, the gradient matching loss, the total variational regularization loss, and the edge preservation loss.

[0009] The present invention also protects a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, can implement the steps of the method.

[0010] Compared with the prior art, the beneficial effects of the present invention are: This invention is for 3D-CT reconstruction of CT projection images of soil and rock media. It is suitable for the characteristics of CT images of soil and rock media (generally with voids and distinct minerals). It can effectively achieve the measurement of the saliency of fine structures, including Gaussian contribution modulation based on detail saliency and residual response, adaptive splitting, and composite loss constraints for preserving micropores, microcracks, and mineral boundaries.

[0011] This invention can significantly improve the ability to identify fine materials and maintain microscopic boundaries, reduce fine structure ambiguity, voxel averaging effect and missed detection of weak absorption phases. It is applicable to CT three-dimensional reconstruction, pore network analysis, fracture identification and digital soil and rock media modeling of shale, sandstone, carbonate rock and soil media samples containing multiple mineral components. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the overall process of the method of the present invention.

[0013] Figure 2 This is a demonstration diagram of the Z-section effect of the test sample of the present invention.

[0014] Figure 3 This is a demonstration diagram of the X-section effect of the test sample of the present invention. Detailed Implementation

[0015] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the scope of protection of the present invention is not limited to the following embodiments.

[0016] This invention provides a method for detail enhancement and reconstruction of CT images of soil and rock media. 1) Acquisition and preprocessing of CT projection data for soil and rock media First, the soil and rock sample to be tested is placed in an industrial micro-CT or laboratory micro-CT system, and multi-angle projection acquisition is performed around the rotation axis to obtain the projection set:

[0017] Where P represents the projection set, Let m represent the m-th projection angle, M be the total number of projections, and (u,v) be the detector plane coordinates.

[0018] Dark field correction, flat field correction, and logarithmic transformation are performed on the original projection to obtain the line integral projection. :

[0019] in, The intensity of the sample projection. For the intensity of the empty field, This is for dark field response. If necessary, ring artifact suppression, bad pixel repair, and noise suppression are performed on the projection to form standard projection data for subsequent optimization.

[0020] 2) Initialization of the three-dimensional Gaussian field The soil and rock medium to be reconstructed is represented as a superposition of N three-dimensional Gaussian elements:

[0021] in, Represents a spatial point x∈R 3 Distribution of linear attenuation coefficient at a given location; This represents the density magnitude of the i-th Gaussian element; Let the i-th three-dimensional Gaussian kernel be defined as:

[0022] in, Let be the covariance matrix of the i-th original Gaussian element, representing the scale and anisotropy of the Gaussian element in space. The superscript -1 indicates the inversion operation. (This is related to the original R...) 2 Unlike GS, this invention employs anisotropic covariance decomposition:

[0023] in, For rotation matrix, The scale of the Gaussian element is controlled in the three principal directions respectively.

[0024] This allows Gaussian elements to better fit directional structures such as fissures, lamellar structures, and slender pore throats.

[0025] During initialization, a coarse reconstruction (such as FDK results or low-resolution SART results) can be used for threshold sampling, and the sample solid region and pore boundary region can be selected as the initial center distribution region.

[0026] 3) Gaussian splash model, outputting predicted projection and predicted density, covariance matrix, and position of Gaussian sphere.

[0027] For a given ray Its projection line integral within the object is:

[0028] Substituting the Gaussian field, we have:

[0029] in, These represent the near and far integration boundaries where the ray enters and leaves the reconstruction region, respectively, and t represents the ray parameter. This represents the prediction line integral corresponding to ray r; Since the integral of the ray and the Gaussian kernel can be transformed into a one-dimensional Gaussian form, this invention uses a method combining analytical approximation and numerical truncation to calculate the contribution of each Gaussian element to the ray:

[0030] Furthermore, to enhance the contribution of fine structures to the projection residuals, a detail-sensitive modulation factor is introduced into the Gaussian splash model. :

[0031]

[0032] In the formula, Let i be the detail significance index of the i-th Gaussian element. Let be the residual response intensity of the i-th Gaussian element. Let i be the projection intensity of the i-th Gaussian element. Here are the weighting coefficients, where .

[0033] 4) Mechanism of enhancement by subtle substances 4.1 Detail Saliency Measurement To detect potential regions of fine matter, a local detail saliency index is defined for each Gaussian element (a weighted sum of the local first-order gradient magnitude, Frobenius norm, and average reprojection error):

[0034] in, This represents the center position vector of the i-th original Gaussian element. Represents the local first-order gradient magnitude. Denotes the Frobenius norm of the Hessian matrix. This represents the average reprojection error of the projection region corresponding to the Gaussian element; These represent the weights. The value ranges from 0 to 1. In this embodiment... , , The values ​​are 0.3, 0.3, and 0.4, respectively, and the sum of the three is 1. In actual use, the weights of the local first-order gradient magnitude and Frobenius norm are adjusted according to the complexity of the boundary of the soil and rock medium (circular or other regular patterns). The two change synchronously. If the boundary is an irregular or complex pattern, the weight increases; if it is a circular or other regular pattern, the weight decreases. By default, the local first-order gradient magnitude, Frobenius norm, and average reprojection error are the corresponding normalized results.

[0035] when Greater than the preset threshold T s (The value ranges from 0 to 1, depending on the specific type of soil and rock medium; the more complex the medium, the larger the value). When this value is found, it is determined that there may be micro-cracks, micro-pores, and fine-grained mineral edges in the area, and Gaussian element splitting is required.

[0036] Residual response strength The weighted average of the projected residuals in the set of rays affected by the i-th Gaussian element is obtained as follows:

[0037] in This represents the set of rays that pass through the influence of the i-th Gaussian element. This represents the weighted average. Represents the predicted projection, Represents the true projection.

[0038] 4.2 Gaussian Element Adaptive Splitting If detail-sensitive modulation factor Greater than the preset sensitivity threshold Then it is considered a region of significant detail ( The recommended value range is between [1.15, 14]. Perform a splitting operation on Gaussian elements in regions of significant detail, and determine whether to perform the splitting operation once every 100 iterations.

[0039] Let the original Gaussian parameters be... Set position offset Then it splits into K sub-Gaussian elements, where K=3 in this embodiment:

[0040]

[0041] in Let K be the density magnitudes of the K sub-Gaussian cells split from the i-th Gaussian cell. Let be the covariance matrix of the k-th sub-Gaussian element split from the i-th Gaussian element. This represents the density magnitude of the i-th Gaussian element; <1, used to control the degree of shrinkage of the sub-Gaussian unit relative to the original Gaussian unit; The position offset is selected along the local principal curvature direction or the residual principal direction. The splitting operation is preferentially performed along the direction corresponding to the largest eigenvalue in the principal covariance axis and the local gradient direction, thereby improving the fitting accuracy of Gaussian elements for slender or sharp fine structures.

[0042] 5) Composite loss function To achieve high-quality CT reconstruction of soil and rock media, this invention constructs the following composite loss function:

[0043] in, For the L1 loss of the projected image, For structural similarity loss, For gradient matching loss; is the total variational regularization loss, and is the original loss function of the Gaussian splash model.

[0044] Edge preservation loss Defined as:

[0045] in, For 3D volume data, x =(a,b,c) are spatial coordinates. for x Predicted density at location, For true density, For spatially varying edge weights, This is the gradient operator.

[0046] 6) Training strategies During training, splitting iteration nodes are set, and during the training densification phase, periodic Gaussian splitting is performed once every splitting iteration node.

[0047] This invention proposes a three-stage training process for the CT reconstruction framework to balance convergence stability and refinement optimization requirements: The warm-up stage covers 0 to 500 iterations (early model training phase), where only initial parameter optimization (i.e., 3D Gaussian field initialization) is performed without any Gaussian compaction, establishing a stable baseline for subsequent optimizations; the compaction stage involves 500 to 15,000 iterations, with periodic Gaussian splitting performed every 100 iterations to adaptively refine the Gaussian structure in detail-rich regions; the refinement stage involves 15,000 to 30,000 iterations, where only Gaussian parameters are refined. Fine-tuning is performed, and the splitting operation is no longer performed. The number of Gaussian spheres is fixed, so the structural characteristics of Gaussian are not changed. This consolidates the reconstruction quality while avoiding overfitting.

[0048] 7) Experimental Results This experiment used CT reconstruction of basalt as the research object, and compared and evaluated the original R... 2 The reconstruction performance of the -GS method and the traditional FDK method at a low number of views (50 views) was compared, with the reconstruction results of 2000 views used as the ground truth (GT) as the benchmark. The experiment employed four quantitative metrics: 3DPSNR, 3DSSIM, 2DPSNR, and 2DSSIM, to comprehensively evaluate the overall accuracy, structural similarity, and detail reproduction of the 2D slices. Experimental results are as follows: Figure 2 and Figure 3 As shown. Figure 2 The Z-axis section of the rock. Figure 3 The figure shows the X-axis cross-section of the rock, with basalt wrapped in a heat-shrink tubing as an example.

[0049] From the perspective of reconstructed visual effects, the FDK method exhibits severe artifacts and loss of detail in the reconstruction results across 50 viewpoints. Fine structures such as micropores and mineral particles are almost indistinguishable, and the overall image signal-to-noise ratio is extremely low. The original R... 2 While the -GS method can restore the overall structure of rocks, it blurs the fine textures in the enclosed areas and lacks boundary continuity. In contrast, this invention (Ours), under low-view conditions, not only completely preserves the macroscopic morphology of the rock but also accurately restores the micropore contours, mineral grain boundaries, and other fine details in the enclosed areas. Its visual effect is closer to the true value (GT) at 2000 Å, and the clarity and continuity of the detailed textures are significantly superior to R. 2 -GS method. Further magnified local images also verify this conclusion: the fine structure reconstructed by the method in this paper has sharper edges and richer texture levels, while R 2-The GS method exhibits significant blurring and information loss in local areas.

[0050] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Equivalent substitutions, modifications, or improvements made by those skilled in the art without departing from the spirit and substance of the present invention should fall within the scope of protection of the present invention.

[0051] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for detail enhancement and reconstruction of CT images of soil and rock media, characterized in that, The method includes the following: Acquire and preprocess CT projection data of soil and rock media; The soil and rock medium to be reconstructed is represented as a superposition of N three-dimensional Gaussian elements, and three-dimensional Gaussian initialization is performed; Introducing a detail-sensitive modulation factor into the Gaussian splash model During the densification training phase, if the detail-sensitive modulation factor is greater than a preset sensitivity threshold, it is considered a salient region. Gaussian units within this salient region are then split according to a set splitting iteration node. Through iterative optimization, the trained Gaussian splash model is obtained. The trained Gaussian splash model is used for subsequent CT reconstruction of soil and rock media, outputting the predicted projection and the corresponding Gaussian element predicted density and Gaussian element covariance matrix of the soil and rock media.

2. The method according to claim 1, characterized in that, The detail-sensitive modulation factor Based on detail significance index and residual response intensity The weighted sum and determination; the detailed significance index The residual response intensity is determined by a weighted sum of the local first-order gradient magnitude, Frobenius norm, and average reprojection error of each Gaussian element; It is obtained by weighted averaging of the projected residuals in the set of rays affected by each Gaussian element.

3. The method according to claim 2, characterized in that, The detail-sensitive modulation factor for: ； In the formula, Let i be the detail significance index of the i-th Gaussian element. Let be the residual response intensity of the i-th Gaussian element. The projection intensity of the i-th Gaussian element, , These are the weighting coefficients; ， ， in, This represents the center position vector of the i-th original Gaussian element. Represents the local first-order gradient magnitude. Denotes the Frobenius norm of the Hessian matrix. This represents the average reprojection error of the projection region corresponding to the Gaussian element; These represent the weights respectively; This represents the set of rays that pass through the influence of the i-th Gaussian element. This represents the weighted average. Represents the predicted projection, Represents the true projection.

4. The method according to claim 1, characterized in that, During training, the loss function is a composite loss function consisting of the weighted sum of the L1 loss of the projected image, the structural similarity loss, the gradient matching loss, the total variational regularization loss, and the edge preservation loss.

5. The method according to claim 4, characterized in that, The composite loss function is: ， in, For the L1 loss of the projected image, For structural similarity loss, For gradient matching loss, The total variational regularization loss; Edge preservation loss is defined as: ， in, For 3D volume data, x =(a,b,c) are spatial coordinates. for x Predicted density at location, For true density, For spatially varying edge weights, This is the gradient operator.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program can perform the steps of the method described in any one of claims 1-5.

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