Method for analyzing internal structure of luneberg lens based on high-resolution X-ray and 3D Gaussian algorithm

Abstract

The invention discloses a method for analyzing the internal structure of a Longbour lens based on high-resolution X-ray and a 3D Gaussian algorithm, and relates to the technical field of optical lenses, and the method comprises the following specific implementation steps: S1, configuring an RGB-X-ray combined imaging system, and carrying out the data collection, S2, carrying out the calibration of the external parameters of a camera through a calibration plate, and carrying out the calculation of the internal structure of the Longbour lens. According to the method, X-ray scanning is carried out on the lens to obtain the multi-direction projection images, fitting is carried out on the three-dimensional projection data based on the Gaussian function and the Gaussian mixture model, high-precision reconstruction of all spaces in the lens is achieved, the limitation of traditional X-ray tomography in the aspects of limited resolution, noise interference and reconstruction artifacts is effectively solved, and high-precision reconstruction of all the spaces in the lens is achieved. Errors caused by discretization or interlayer interfaces in a traditional voxel reconstruction method are avoided, high-resolution, stable and reliable three-dimensional representation can be kept even under the condition of a complex structure or a large-size lens, and the measurement precision and reliability of the internal structure of the lens are remarkably improved.

Description

A Method for Analyzing the Internal Structure of Luneburg Lenses Based on High-Resolution X-rays and 3D Gaussian Algorithms Technical Field

[0001] This invention relates to the field of optical lens technology, specifically to a method for analyzing the internal structure of Luneburg lenses based on high-resolution X-rays and 3D Gaussian algorithms. Background Technology

[0002] Due to its unique omnidirectional focusing characteristics, low aberrations, and wide bandwidth applicability, the Luneburg lens has shown great application prospects in many fields such as optical imaging, communication antennas, and space optics. This optical element has extremely high requirements for the three-dimensional continuous distribution of the refractive index inside the material. In the current processing and verification of Luneburg lenses, the typical approach is to use X-rays or miniature CT to perform tomographic scanning on the lens.

[0003] The imaging and reconstruction process of CT has obvious limitations in fine optical materials. On the one hand, CT is affected by the projection angle and relies on strict system geometric calibration. Once it is obstructed or the projection angle is insufficient, the reconstruction quality will be significantly reduced. Moreover, the voxel data generated by the algorithm is difficult to fit in X-ray tomography. On the other hand, CT reconstruction is prone to producing stripe artifacts and halos near the interface, resulting in unrealistic edge transitions and discontinuous density curves, which in turn leads to model degradation.

[0004] To avoid the aforementioned technical problems, it is indeed necessary to provide a method for analyzing the internal structure of Luneburg lenses based on high-resolution X-rays and 3D Gaussian algorithms to overcome the deficiencies in the prior art. Summary of the Invention

[0005] This invention provides a method for analyzing the internal structure of Luneburg lenses based on high-resolution X-rays and 3D Gaussian algorithms. It can effectively solve the problems mentioned in the background art, such as the influence of projection angle on CT and the reliance on strict system geometric calibration. Once obstructed or with insufficient projection angle, the reconstruction quality will significantly decrease. In addition, the voxel data generated by the algorithm is difficult to fit in X-ray tomography, and CT reconstruction is prone to producing stripe artifacts and halos near the interface, resulting in unrealistic edge transitions, discontinuous density curves, and thus model deterioration.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for analyzing the internal structure of a Luneburg lens based on high-resolution X-rays and a 3D Gaussian algorithm, comprising the following specific implementation steps:

[0007] S1. Configure an RGB-X-ray combined imaging system for data acquisition;

[0008] S2. Calibrate the camera's external parameters using the calibration board;

[0009] S3. Obtain the initial 3D point cloud using the cube initialization method;

[0010] S4. Reconstruct the internal structure of the Luneburg lens using a 3D Gaussian modeling system;

[0011] S5. Output and measure spatial density information.

[0012] According to the above technical solution, in step S3, the three-dimensional reconstruction space is uniformly sampled by a cube initialization method to construct an initial three-dimensional Gaussian set to represent the density distribution inside the lens.

[0013] According to the above technical solution, in step S4, the Gaussian parameters are iteratively optimized by constructing an objective function that includes data consistency terms and prior constraint terms.

[0014] According to the above technical solution, in step S5, the final Gaussian point is used as the input parameter to calculate the spatial density distribution;

[0015] The entire lens volume is divided into discrete voxels, each corresponding to a fixed spatial position. First, for each voxel, its relative distance to the center position of all Gaussian points is calculated.

[0016] Secondly, based on the transparency α and radiation intensity of the Gaussian points, the contribution value of each Gaussian point is obtained. The contributions of all Gaussian points within the voxel are accumulated according to the distance value to obtain the density value of the voxel. In this process, Gaussian points with minimal contributions are ignored to maintain the stability of the density calculation.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: by obtaining multi-directional projection images through X-ray scanning of the lens, and fitting the three-dimensional projection data based on Gaussian function and Gaussian mixture model, high-precision reconstruction of each space inside the lens is achieved. This effectively solves the limitations of traditional X-ray tomography in terms of limited resolution, noise interference and reconstruction artifacts, and avoids the errors caused by discretization or interlayer interfaces in traditional voxel reconstruction methods. Even in the case of complex structures or large-size lenses, it can maintain high resolution and stable and reliable three-dimensional characterization, and significantly improve the accuracy and reliability of lens internal structure measurement. Attached Figure Description

[0018] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0019] In the attached diagram:

[0020] Figure 1 is a schematic diagram of the overall process of the present invention;

[0021] Figure 2 is a schematic diagram of the calibration plate in this invention;

[0022] Figure 3 is a schematic diagram of the Luneburg lens structure in this invention;

[0023] Figure 4 is a schematic diagram of the imaging of the X camera in this invention;

[0024] Figure 5 is a schematic diagram of the Luneburg lens reconstruction process in this invention. Detailed Implementation

[0025] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0026] Example 1:

[0027] As shown in Figures 1, 4, and 5, this invention provides a technical solution: a method for analyzing the internal structure of a Luneburg lens based on high-resolution X-rays and a 3D Gaussian algorithm, comprising the following specific implementation steps:

[0028] S1. Configure an RGB-X-ray combined imaging system for data acquisition;

[0029] S2. Calibrate the camera's external parameters using the calibration board;

[0030] S3. Obtain the initial 3D point cloud using the cube initialization method;

[0031] S4. Reconstruct the internal structure of the Luneburg lens using a 3D Gaussian modeling system;

[0032] S5. Output and measure spatial density information.

[0033] In S1, the lens to be tested is fixed on the scanning bracket so that it is always within the common field of view of the X-ray camera and the RGB visible light camera during rotation and movement. The scanning system of this embodiment adopts the coaxial arrangement of the RGB camera and the X-ray camera so that the two types of images can be acquired synchronously under the same geometric conditions.

[0034] During the scanning process, the system applies X-rays to the lens to obtain multi-angle projection images of its internal structure. At the same time, it uses an RGB camera to simultaneously capture the texture and outline information of the lens's outer surface. Through this collaborative imaging method, an X-ray projection sequence covering the entire volume of the lens and its corresponding RGB image sequence are obtained, where each frame of the image corresponds to the same scanning angle.

[0035] The acquired multimodal images are preprocessed, including but not limited to denoising, geometric correction, cross-modal registration, exposure compensation, and data augmentation, to improve the usability and alignment accuracy of the images and provide consistent and reliable input data for subsequent 3D reconstruction and Gaussian modeling.

[0036] In S2, a specially designed calibration plate that can be used for both visible light and X-ray imaging is employed. The ArUco markings on the calibration plate are made of high-density, radiopaque material, forming a clear outline in the X-ray image. The X-ray-transmitting part of the markings is painted white, and the radiopaque part is painted black to enhance the recognizability of the X-ray image. The rest of the calibration plate is made of X-ray-transmitting material, and the RGB camera can normally observe the markings and the texture of the plate surface. Based on this structure, the same marking system can be detected by two imaging modalities at the same time, thereby realizing cross-modal calibration.

[0037] First, the calibration board is placed in the RGB-X-ray joint imaging system, and multiple frames of RGB images and multiple frames of X-ray images are acquired respectively. In the RGB images, by detecting the visible marks on the calibration board and combining them with their known spatial geometry, the extrinsic parameters of the RGB camera in the calibration board coordinate system can be obtained using the PnP method. Correspondingly, in the X-ray images, the two-dimensional pixel positions of the metal marks are extracted based on their projected contours. Similarly, based on the predetermined three-dimensional points of the calibration board, the extrinsic parameter matrix of the X-ray camera with respect to the calibration board coordinate system is calculated using PnP. Thus, the attitudes of the two types of cameras under the same coordinate reference have been obtained independently.

[0038] Subsequently, the RGB and X-ray images acquired at the same time were paired up. Based on the external parameter relationship between the two relative to the calibration plate, the relative pose transformation between the RGB camera and the X-ray camera was directly calculated. In order to improve the stability and accuracy of cross-modal calibration, the relative transformations obtained from multiple sets of images were fused, such as taking the average transformation and using a joint nonlinear optimization method to constrain the consistency of the overall results and minimize the error.

[0039] After completing the pose calibration between the cross-modal cameras, imaging of the lens can be carried out. Several visible light markers are pre-added to the lens structure. These markers can be detected by the image acquired by the RGB camera. Combined with their predetermined three-dimensional position in the lens coordinate system, the extrinsic parameters of the RGB camera relative to the lens coordinate system are obtained by PnP. Since the relative transformation between RGB and X-ray camera has been calibrated in the previous step, the extrinsic parameters of the RGB camera are transformed to the X-ray camera coordinate system, thereby obtaining the extrinsic parameter information of the X-ray camera in the lens coordinate system.

[0040] In S3, the three-dimensional reconstruction space is uniformly sampled using a cube initialization method to construct an initial three-dimensional Gaussian set to represent the density distribution inside the lens;

[0041] The specific steps are as follows:

[0042] First, the intrinsic and extrinsic parameter matrices corresponding to each projection are calculated using the geometric parameters of the X-ray scanner to achieve accurate calibration of the imaging model. Then, a three-dimensional cubic mesh that can completely enclose the lens volume is defined, and the cube size, resolution, and grid spacing are determined. 3D points are uniformly sampled in the above cubic mesh, and these points are used as the center positions of the Gaussian point cloud. The covariance matrix and transparency are initialized for each point, and the eigenvectors are randomly initialized to represent the radiation characteristics of the points. In addition, the projection error is used as the optimization objective to update the center position, density parameters, and scale parameters of each three-dimensional Gaussian unit to suppress noise and unreasonable density areas, making the results more consistent with the structure of real objects. In this way, a continuous differentiable mapping from Gaussian point cloud to two-dimensional projection image is achieved, providing the possibility for gradient optimization.

[0043] In S4, the Gaussian parameters are iteratively optimized by constructing an objective function that includes data consistency terms and prior constraint terms. The specific steps are as follows:

[0044] S401, Gaussian Point Cloud Rendering: For X-ray projection data, the spherical harmonic function in the original Gaussian distribution is simplified, and the physical properties are represented by the feature vectors of Gaussian points. This reduces computational complexity and more closely reflects the physical characteristics of X-ray imaging. The radiation intensity of each Gaussian point is calculated using the Radioactive Impulse Response (RIRF) function. This function takes the features of the Gaussian point as input and can simulate the contribution of the point cloud to the pixel during the projection process, taking into account the attenuation and transparency effects of X-rays. Subsequently, the initialized Gaussian point cloud input (DRR) module is used to project and render all Gaussian points. During the projection process, for each pixel, the DRR accumulates the contribution of all Gaussian points projected to that pixel, performs transparency-weighted accumulation in order from near to far, and combines transparency and radiation intensity to calculate the actual radiation impact of each point on the pixel, thereby realizing the physical simulation and pixel-level fusion of the X-ray projection process.

[0045] S402. Constructing Image Loss: During training, the rendered image is first compared with the real X-ray projection image. Specifically, the L1 loss of each pixel is calculated to measure the difference in pixel intensity. At the same time, the structural similarity (SSIM) loss between the rendered image and the real projection image is calculated to evaluate the structural consistency of the overall image. Then, the L1 loss and SSIM loss are weighted and combined according to the hyperparameter γ to form the total training loss, which is used as the optimization objective to guide the iterative update of the Gaussian model parameters.

[0046] S403. Constructing a regularization loss term: To ensure the stability and physical rationality of the Gaussian model, a series of constraints are imposed on the Gaussian points. First, the center position of the Gaussian points is restricted, so that they can only move within the effective area of ​​the object, thereby preventing the final model from deviating from the actual structure. At the same time, a sparsity constraint is imposed on the transparency of the Gaussian points to suppress the contribution of redundant points and improve the sparsity and efficiency of rendering. Finally, in order to maintain the local continuity of the point cloud and prevent isolated or abruptly changing points, a smoothing constraint is imposed on the feature differences between each Gaussian point and its neighborhood, further improving the accuracy and interpretability of the reconstruction results.

[0047] S404, Phased Training Strategy: During training, a phased optimization strategy is adopted to improve rendering accuracy and ensure model stability. In the early stage of training, only the transparency and feature vectors of Gaussian points are updated, focusing on learning the radiation intensity distribution to quickly learn the radiation distribution inside the lens, avoiding premature adjustments to the center position and shape that could lead to training instability. In the middle stage of training, the center position and covariance matrix of Gaussian points are gradually unfrozen, enabling the Gaussian point cloud to adapt to the complex density changes inside the lens, thereby more accurately fitting continuous gradients and local structures. In the later stage of training, various regularization constraints are strengthened, and Gaussian points with minimal contributions are pruned to achieve sparsity and improved stability of the Gaussian point cloud. At the same time, throughout the entire training process, the number of Gaussian points is dynamically adjusted through an adaptive strategy to balance computational efficiency while ensuring rendering accuracy.

[0048] In S5, the final Gaussian point is used as the input parameter to calculate the spatial density distribution;

[0049] To reduce computational load and avoid unnecessary computational overhead, the entire lens volume is divided into discrete voxels, each corresponding to a fixed spatial location. First, for each voxel, its relative distance to the center of all Gaussian points is calculated. Second, based on the transparency α and radiation intensity of the Gaussian points, the contribution value of each Gaussian point is obtained. The contributions of all Gaussian points within the voxel are accumulated based on the distance value to obtain the density value of that voxel. In this process, Gaussian points with minimal contributions are ignored to maintain the stability of the density calculation.

[0050] Example 2:

[0051] As shown in Figures 2 and 3, the method for analyzing the internal structure of a Luneburg lens based on high-resolution X-rays and a 3D Gaussian algorithm provided in this embodiment of the invention includes the following steps:

[0052] In this embodiment, a single X-ray camera and a single RGB camera are used. The Lumpur lens is fixedly placed in the center of the rotating disk. The disk is driven to rotate in fixed-angle steps to obtain multi-angle imaging data covering the entire lens. All image acquisition is completed within the same time period to ensure stable illumination. Vibration of the equipment must be avoided during the acquisition process.

[0053] In this embodiment, in order to enable a single RGB camera to obtain the extrinsic parameters in the experimental system, an extrinsic parameter calibration method based on a "labeled sphere (Lumberjack lens)" is proposed. This scheme utilizes a three-dimensional curved surface with a known radius on the surface of the sphere, and regularly attaches multiple marker points on the sphere. Since the three-dimensional position of each marker point in the spherical coordinate system is known, and the center of the sphere can be used as the natural world coordinate origin, the three-dimensional-two-dimensional projection relationship can be solved by two-dimensional imaging of these marker points in a single RGB image, thereby recovering the extrinsic parameters of the RGB camera.

[0054] In this embodiment, since the Lumborghäuser lens itself is a standard sphere, there is no need to place a separate calibration sphere; the lens can be used directly as a natural calibration device.

[0055] Let the radius of the sphere be R, and the center of the sphere be defined as the origin of the world coordinate system. N marker points are attached to the surface of the sphere, and their three-dimensional positions in the world coordinate system are denoted as:

[0056]

[0057] Each point satisfies the spherical constraint:

[0058]

[0059] The spatial distribution of marker points can be pre-designed according to the latitude and longitude parameterization method of the sphere to ensure that they are evenly distributed in all directions of the sphere, thereby enhancing the observability and stability of the external parameter solution;

[0060] Suppose that the spherical mark captured by the RGB camera forms a two-dimensional point in the image plane. Then a set of three-dimensional–two-dimensional corresponding point pairs can be obtained:

[0061]

[0062] Let the RGB camera intrinsic parameter matrix be... Its external reference This can be achieved by minimizing the reprojection error of all marked points:

[0063]

[0064] in, This represents the perspective projection operation from 3D camera coordinates to 2D image coordinates, assuming a 3D point... First, normalization is performed;

[0065]

[0066] Given camera intrinsic parameters:

[0067]

[0068] but:

[0069]

[0070] In this embodiment, an RGB camera and an X-ray camera are installed simultaneously in the experimental setup to ensure that the camera centers are relatively fixed, since the unique relative pose transformation matrix between the two cameras has been obtained in advance. Let the extrinsic parameters of the RGB camera be... The external parameters of the X-ray camera are ,but:

[0071]

[0072] Meanwhile, in principle, the centers of the two cameras should be the same point in three-dimensional physical space. Therefore, the point of the X-ray camera can be projected into three-dimensional space for verification. Let the coordinates of the center of the sphere on the X-ray image plane be... The radius of the sphere in the image is The physical radius of the sphere is The rotation and translation matrix of the X-ray camera is Then the three-dimensional center coordinates of the sphere are:

[0073]

[0074] in, The equivalent focal length (which can be taken as the type of X-ray system) is... (the average of the two).

[0075] At the same time, the three-dimensional position of the sphere's center in the RGB camera coordinate system can be obtained. The accuracy of the calculated relative transformation matrix can be measured by the difference between the two.

[0076] In this embodiment, based on the camera's imaging parameters and projection geometry, the size and center position of the lens in three-dimensional space can be approximately determined. Based on this information, a three-dimensional cuboid region that can completely surround the lens is constructed, and its size is denoted as [missing information]. Assuming the center of the cuboid is To initialize a 3D Gaussian point cloud in this space, a regular mesh is created on the cuboid with a fixed step size d, and samples are taken in three directions:

[0077]

[0078] in, The values ​​are integers, and the above three-dimensional sampling points are used as the center coordinates of the initial Gaussian point cloud;

[0079] In this example, since there is no need to recover surface color information, the traditional 3D Gaussian representation is adaptively modified: the spherical harmonic illumination term in the original model is removed, and a learnable radiation feature vector is introduced to describe the radioactive response characteristics of X-ray Gaussian points. The parameterized structure of each Gaussian point can be defined as follows:

[0080]

[0081] in, The location of the Gauss point. Let covariance matrix be the variance matrix. Its opacity coefficient, As an eigenvector representing local radiation characteristics, in the above formula, f, like Gaussian position, covariance, and transparency, is a parameter that is being optimized.

[0082] Radiation intensity at each Gaussian point Its learnable radiative eigenvectors The result is obtained after calculation using the mapping function:

[0083]

[0084]

[0085] By combining an X-ray imaging model and utilizing the camera's intrinsic and extrinsic parameters, a 3D Gaussian point cloud is projected onto a 2D imaging plane, achieving differentiable rendering for each pixel. The final rendered value is determined by the cumulative contribution of all Gaussian points on the ray path corresponding to that pixel, which can be expressed as:

[0086]

[0087] in, This represents the rendered image;

[0088] For a differentiable rendering model, given a ray:

[0089]

[0090] in, For X-ray camera source point, Indicates the direction of the ray;

[0091] For the j-th Gaussian point, its spatial location The volume density at that location is:

[0092]

[0093] in, Let j be the centroid of the j-th Gaussian point; Here is the covariance matrix:

[0094]

[0095] in, Indicates the orientation of the Gaussian ellipsoid. This represents the standard deviation of the ellipsoid along the principal axis.

[0096] Each Gaussian point contributes opacity information (obtained from point features through a small network and linear mapping), and the final value (without considering noise) is the weighted sum of all Gaussian points along the ray:

[0097]

[0098] The goal of this embodiment is to make the rendered projected image as consistent as possible with the actual acquired X-ray GT image in pixel space. Therefore, the overall loss function is constructed as follows:

[0099]

[0100] Used to constrain pixel-level intensity errors, ensuring that the reconstructed result remains consistent with the true projection at a level of detail. To improve structural consistency and ensure that the overall imaging pattern matches the ground truth (GT) image, a three-dimensional density distribution consistent with the internal structure of the real object can be gradually obtained by jointly optimizing the position, covariance, transparency, and radiometric characteristics of Gaussian points. It is a hyperparameter used to balance the importance of the two loss terms;

[0101] Define the half-dimension on each coordinate axis as:

[0102]

[0103] To prevent Gaussian points from drifting outside the effective boundary of the object during optimization, this embodiment applies ReLU penalties to the out-of-bounds portions of the Gaussian points in the three coordinate axes. The regularization term can be expressed as:

[0104]

[0105] To suppress redundant Gaussian points and improve model sparsity and rendering efficiency, this embodiment sets a sparsity penalty on its opacity. When the opacity is below a preset threshold... At this point, points that do not contribute will be further pushed to be gradually removed during the iteration process, and its regularization form is:

[0106]

[0107] The applied neighborhood smoothing regularization term is:

[0108]

[0109] in, For the first The neighborhood set of Gaussian points The radiation intensity at the Gaussian point. Neighborhood weights are typically set based on the distance between points:

[0110]

[0111] in Let the coordinates be the center coordinates of the Gaussian point. It is a constant, controlling the smoothing radius;

[0112] The three types of regularization terms together constitute the total constraint term, which can be expressed as:

[0113]

[0114] in, , , These are the weight coefficients of the three regularization terms.

[0115] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the internal structure of Luneburg lenses based on high-resolution X-rays and 3D Gaussian algorithm, characterized by: The specific implementation steps are as follows: S1, Configure the RGB-X-ray joint imaging system and collect data; S2, Calibrate the camera extrinsic parameters using a calibration board; S3, Obtain the initial 3D point cloud using the cube initialization method; S4, Reconstruct the internal structure of the Luneburg lens using a 3D Gaussian modeling system; S5, Output and measure the spatial density information.

2. The method for analyzing the internal structure of a Luneburg lens based on high-resolution X-rays and a 3D Gaussian algorithm according to claim 1, characterized in that: In step S3, the three-dimensional reconstruction space is uniformly sampled using a cube initialization method to construct an initial three-dimensional Gaussian set representing the density distribution inside the lens.

3. The method for analyzing the internal structure of a Luneburg lens based on high-resolution X-rays and a 3D Gaussian algorithm according to claim 1, characterized in that: In step S4, the Gaussian parameters are iteratively optimized by constructing an objective function that includes data consistency terms and prior constraint terms.

4. The method for analyzing the internal structure of a Luneburg lens based on high-resolution X-rays and a 3D Gaussian algorithm according to claim 1, characterized in that: In step S5, the final Gaussian point is used as the input parameter to calculate the spatial density distribution. The entire lens volume is divided into discrete voxels, each corresponding to a fixed spatial position. First, for each voxel, its relative distance to the center position of all Gaussian points is calculated. Second, based on the transparency α and radiation intensity of the Gaussian points, the contribution value of each Gaussian point is obtained. The contributions of all Gaussian points within the voxel are accumulated based on the distance value to obtain the density value of that voxel. In this process, Gaussian points with minimal contributions are ignored to maintain the stability of the density calculation.

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